Department of Mathematics, Spring_2016
https://services.math.duke.edu/mcal?listgroup-0
Department of Mathematics Upcoming Seminarsen-us2024-03-28T12:57:34-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyThe motivation behind this semester's working seminar on the Hwang-Mok program.
https://services.math.duke.edu/mcal?abstract-9394
I will give a brief introduction to Hwang and Mok's program to study the geometry of uniruled projective manifolds via their varieties of minimal rational tangents (VMRT). The working seminar is motivated by the idea that there may be an analogous program to study variations of Hodge structure via the characteristic varieties introduced by Sheng and Zuo. As evidence for the proposed program's viability I will show how characteristic varieties may be used to characterize the families of Calabi-Yau manifolds that solve Gross's geometric realization problem for Hermitian symmetric domains.<a href="mailto:robles@math.duke.edu">Colleen Robles</a> (Duke University)2016-01-12T16:30:00-05:009394geometry/topologyGeometry/topology SeminarSpring, 2016Tue, 12 Jan 2016 17:30:00 ESTTuesday, January 12, 2016, 4:30pmTue, 12 Jan 2016 16:30:00 EST119 PhysicsL-functions of Siegel modular forms on GSp(6)
https://services.math.duke.edu/mcal?abstract-9209
I will discuss my work to establish some of the basic analytic properties (finiteness of poles and functional equation) of the Spin L-function of Siegel modular forms on GSp(6). The proof, which is via the Rankin-Selberg method, involves the arithmetic invariant theory of orders in quaternion algebras and a construction Freudenthal used to explicitly realize some of the exceptional groups.Aaron Pollack (Stanford)2016-01-13T13:30:00-05:009209Number TheoryNumber Theory SeminarWed, 13 Jan 2016 13:30:00 EST119 PhysicsWed, 13 Jan 2016 14:30:00 ESTSpring, 2016Wednesday, January 13, 2016, 1:30pmGlassy slowdown and amorphous order
https://services.math.duke.edu/mcal?abstract-9418
Upon approaching the glass transition a liquid gets extremely sluggish
without obvious structural changes. Despite decades of work, the physical
origin of this glassy slowdown remains controversial. A common explanation
relies on the increasing roughness of the underlying free-energy landscape,
but the theoretical and experimental underpinnings of this scenario are
still lacking. In this talk, I will survey recent advances that let us
unambiguously identify and track the growing amorphous order, a
manifestation of the rarefaction of metastable states in the rugged
landscape. I will further explore the crucial role this order plays in
driving the glassy slowdown.<a href="https://scholar.google.com/citations?user=EY0J8s0AAAAJ&hl=en">Sho Yaida</a> (Dept of Chemistry, Duke University)2016-01-19T15:00:00-05:009418CNCSCNCS Seminar119 PhysicsTue, 19 Jan 2016 15:00:00 ESTTuesday, January 19, 2016, 3:00pmTue, 19 Jan 2016 16:00:00 ESTSpring, 2016The norm of structured random matrices
https://services.math.duke.edu/mcal?abstract-9410
Understanding the spectral norm of random matrices is a problem of basic interest in several areas of pure and applied mathematics. While the spectral norm of classical random matrix models is well understood, existing methods almost always fail to be sharp in the presence of nontrivial structure. In this talk, I will discuss new bounds on the norm of random matrices with independent entries that are sharp under mild conditions. These bounds shed significant light on the nature of the problem, and make it possible to easily address otherwise nontrivial phenomena such as the phase transition of the spectral edge of random band matrices. I will also discuss some conjectures whose resolution would complete our understanding of the underlying probabilistic mechanisms.Ramon van Handel (Princeton)2016-01-20T11:15:00-05:009410probabilityProbability SeminarWednesday, January 20, 2016, 11:15amSpring, 2016Wed, 20 Jan 2016 12:15:00 ESTR. J. Reynolds Auditorium, FuquaWed, 20 Jan 2016 11:15:00 ESTKuznetsov, higher weight and exponential sums on GL(3)
https://services.math.duke.edu/mcal?abstract-9313
I will discuss the relationship between the Kuznetsov formula and
certain exponential sums that arise naturally on GL(3). This will lead us to consider the structure of GL(3) Maass forms having non-trivial dependence on the SO(3) part of the Iwasawa decomposition.Jack Buttcane (SUNY Buffalo)2016-01-20T13:30:00-05:009313Number TheoryNumber Theory SeminarWednesday, January 20, 2016, 1:30pmWed, 20 Jan 2016 14:30:00 ESTSpring, 2016119 PhysicsWed, 20 Jan 2016 13:30:00 ESTSeismic wave estimation for buried target detection
https://services.math.duke.edu/mcal?abstract-9436
We introduce an algorithm for buried target detection in the presence of induced seismic waves. Ground fluctuations are measured with an array of laser Doppler vibrometers (LDVs) to estimate the presence of buried objects. Buried targets cause scattering of the subsurface waves, resulting in anomalies in LDV measurements. The seismic wave response depends upon many factors that are rarely known in advance, and drastically affects features used for target classification. We introduce a statistical method that identifies the travelling wave, and anomalies in its propagation. Using standard pattern recognition methods, the proposed algorithm is shown to improve target detection performance over the raw data.Miles Crosskey (CoVar Applied Technologies)2016-01-21T11:45:00-05:009436Data DialogueData DialogueThu, 21 Jan 2016 11:45:00 ESTGross 330Thu, 21 Jan 2016 12:45:00 ESTSpring, 2016Thursday, January 21, 2016, 11:45amComputing Integrals on Surfaces
https://services.math.duke.edu/mcal?abstract-9428
Suppose you need to compute an integral over a general surface numerically.
How would you do it? You could triangulate the surface, or you might use
coordinate charts. Either way is a lot of work, maybe more than you want to do
if you have a large number of surfaces. I will describe a fairly simple method,
appropriate for smooth, closed surfaces, developed by a former grad student here, Jason Wilson, in his Ph.D. thesis, including proofs that his algorithm works. I will then discuss the extension to integrals for potentials defined by densities on surfaces, such as harmonic functions. In that case the integrand has a singularity; special treatment is needed, and some interesting math comes in. Another of our former Ph.D.'s, Wenjun Ying, has contributed to that work (among many projects of his). Such integrals occur in several scientific contexts; I will especially mention Stokes flow (fluid flow dominated by viscosity), appropriate for modeling some aspects of biology on small scales. For more information, see
J. t. Beale, W. Ying, and J. R. Wilson,
A simple method for computing singular or nearly singular integrals on closed surfaces
at my web site or at
http://arxiv.org/abs/1508.00265<a href="mailto:beale@math.duke.edu">Tom Beale</a> (Duke University)2016-01-25T12:00:00-05:009428Graduate-FacultyGraduate/faculty SeminarPhysics 119Mon, 25 Jan 2016 12:00:00 ESTMonday, January 25, 2016, 12:00pmMon, 25 Jan 2016 13:00:00 ESTSpring, 2016Out-of-equilibrium dynamics and statistics of dispersive waves
https://services.math.duke.edu/mcal?abstract-9445
Out-of-equilibrium behavior is the characteristic feature of the long-time dynamics of nonlinear dispersive equations on compact domain. This means that solutions typically do not exhibit any form of long-time stability near equilibrium solutions or configurations. We shall survey several aspects of this behavior both from a dynamical systems and statistical mechanics point of view.Zaher Hani (Georgia Institute of Technology)2016-01-25T16:30:00-05:009445applied math and analysisApplied Math And Analysis SeminarMon, 25 Jan 2016 17:30:00 ESTSpring, 2016Monday, January 25, 2016, 4:30pmMon, 25 Jan 2016 16:30:00 EST119 PhysicsStatistics of abelian varieties over finite fields
https://services.math.duke.edu/mcal?abstract-9450
Joint work with Jacob Tsimerman.
Let B(g,p) denote the number of isomorphism classes of g-dimensional abelian varieties over the finite field of size p. Let A(g,p) denote the number of isomorphism classes of principally polarized g dimensional abelian varieties over the finite field of size p. We derive upper bounds for B(g,p) and lower bounds for A(g,p) for p fixed and g increasing. The extremely large gap between the lower bound for A(g,p) and the upper bound B(g,p) implies some statistically counterintuitive behavior for abelian varieties of large dimension over a fixed finite field.Mike Lipnowski (Duke University)2016-01-27T13:30:00-05:009450Number TheoryNumber Theory SeminarSpring, 2016Wed, 27 Jan 2016 14:30:00 ESTWednesday, January 27, 2016, 1:30pmWed, 27 Jan 2016 13:30:00 EST119 PhysicsLarge deviations, moderate deviations, and importance sampling
https://services.math.duke.edu/mcal?abstract-9403
Importance sampling is an accelerated Monte Carlo algorithm that can reduce variance when estimating small probabilities. The design of the algorithm involves the choice of a change of measure, and based on this choice the performance can range from substantially better than standard Monte Carlo to substantially worse. One approach to choosing a change of measure involves embedding the problem of interest in a sequence of processes that satisfies a large deviations principle, and then basing the change of measure on subsolutions to the Hamilton-Jacobi-Bellman equation associated the large deviations rate function. This approach has the benefit of guaranteeing a certain level of asymptotic performance based on the subsolution, but different embeddings can lead to different rate functions, subsolutions, and consequently different algorithms. I will contrast the strengths and weaknesses of two different embeddings, one using a scaling commonly referred to as the standard large deviations scaling and the other using a scaling referred to as moderate deviations.Dane Johnson (UNC - Chapel Hill)2016-01-28T16:30:00-05:009403probabilityProbability SeminarThu, 28 Jan 2016 16:30:00 EST119 PhysicsSpring, 2016Thu, 28 Jan 2016 17:30:00 ESTThursday, January 28, 2016, 4:30pmOptimal reservoir conditions for material extraction across pumping and porous channels
https://services.math.duke.edu/mcal?abstract-9458
In this talk, I will discuss a new result in fluid flows through channels with permeable membranes with simple pumping dynamics. Fluid will be exchanged and metabolized in a simple reservoir and I will demonstrate the existence of optimal reservoir properties that may either maximize or minimized the amount of fluid being extracted across the channel walls.
The biological relevance of this work may be seen by noting that all living organisms of a sufficient size rely on complex systems of tubular networks to efficiently collect, transport and distribute nutrients or waste. These networks exchange material with the interstitium via embedded channels leading to effective permeabilities across the wall separating the channel interior from the interstitium. In many invertebrates, for example, respiratory systems are made of complex tracheal systems that branch out through the entire body allowing for passive exchange of oxygen and carbon dioxide. In many of these systems, certain animals utilize various pumping mechanisms that alter the flow of the air or fluid being transported. Although the net effect of pumping of the averaged rates of fluid flow through the channel is typically well understood, it is still a largely open problem to understand how, and in what circumstances, pumping enables and enhances the exchange of material across channel walls. It has been demonstrated experimentally, for example, that when certain insects flap their wings, compression of the trachea allow for more efficient oxygen extraction, however it is unclear if this pumping is optimized for flight, oxygen uptake or neither, and understanding this problem quantitatively will shed insight on this biological process. Many of these interesting scenarios occur at low Reynolds number and this regime will be the focus of the presentation.Gregory Herschlag (Duke University)2016-01-29T12:00:00-05:009458mathematical biologyMathematical Biology SeminarSpring, 2016Fri, 29 Jan 2016 13:00:00 ESTFriday, January 29, 2016, 12:00pmFri, 29 Jan 2016 12:00:00 EST119 PhysicsAn Introduction to the Riemann-Hilbert Correspondence
https://services.math.duke.edu/mcal?abstract-9489
Early in the history of complex analysis, it was realized that there are
no continuous versions of the square root or the logarithm on the entire
complex plane; instead, analysts invented multi-valued functions to deal
with these strange behaviors. The "graphs" of these multi-valued
functions can get very interesting, and can be interpreted
topologically. In general, the space of solutions to a "nice" system of
holomorphic ordinary differential equations on the non-zero complex
numbers will not be made up of functions, but of multi-functions.
Studying these spaces of solutions have led to several ideas in
algebraic topology, especially monodromy, and the relationship between
systems of ODE and possible monodromies is called the Riemann-Hilbert
Correspondence.<a href="http://fds.duke.edu/db/aas/math/grad/jdc73">Joshua Cruz</a> (Duke University)2016-02-01T12:00:00-05:009489Graduate-FacultyGraduate/faculty SeminarMon, 01 Feb 2016 13:00:00 ESTSpring, 2016Monday, February 1, 2016, 12:00pmMon, 01 Feb 2016 12:00:00 EST119 PhysicsHigh order asymptotic preserving methods for some kinetic models
https://services.math.duke.edu/mcal?abstract-9338
Many problems in science and engineering involve parameters in their mathematical models. Depending on the values of the parameters, the equations can differ greatly in nature. Asymptotic preserving (AP) methods are one type of methods which are designed to work uniformly with respect to different scales or regimes of the equations when the parameters vary. <br/><br/>
In this talk, I will present our work in developing high order AP methods for some kinetic models, including discrete-velocity models in a diffusive scaling and the BGK model in a hyperbolic scaling. When the Knudson number approaches zero, the limiting equations of the former model can be heat equation, viscous Burgers equation, or porous medium equation, while the limiting equations for the latter are the compressible Euler equations. When the Knudson number is very small, the BGK model also leads to compressible Navier-Stokes equations. The proposed methods are built upon a micro-macro decomposition of the equations, high order discontinuous Galerkin (DG) spatial discretizations, and the globally stiffly accurate implicit-explicit Runge-Kutta (IMEX-RK) temporal discretizations. Theoretical results are partially established for uniform stability, error estimates, and rigorous asymptotic analysis. Numerical experiments will further demonstrate the performance of the methods.Fengyan Li (Rensselaer Polytechnic Institute)2016-02-01T16:30:00-05:009338applied math and analysisApplied Math And Analysis SeminarMon, 01 Feb 2016 16:30:00 EST119 PhysicsMon, 01 Feb 2016 17:30:00 ESTSpring, 2016Monday, February 1, 2016, 4:30pmSingularities of Lagrangian Mean Curvature Flow
https://services.math.duke.edu/mcal?abstract-9382
In a Calabi-Yau manifold, mean curvature flow--the downward gradient for the area functional--preserves the Lagrangian condition. Thus Lagrangian mean curvature flow suggests a way to find minimal Lagrangian submanifolds of a CY manifold, provided the flow lasts for all time.
However, finite-time singularities are expected along the flow; in fact, ill-behaved singularities are generic in some sense. In this talk we will discuss two main results: one, that type I (mild) finite-time singularities can be predicted by looking the cohomology of the initial Lagrangian submanifold, and two, that type II (ill-behaved) singularities can be modeled as unions of special Lagrangian cones. We will also discuss what these results say about using mean curvature flow to understand the topology of Lagrangian submanifolds.<a href="http://www4.ncsu.edu/~aacoope2/">Andrew Cooper</a> (North Carolina State University)2016-02-02T16:30:00-05:009382geometry/topologyGeometry/topology SeminarTue, 02 Feb 2016 16:30:00 EST119 PhysicsSpring, 2016Tue, 02 Feb 2016 17:30:00 ESTTuesday, February 2, 2016, 4:30pmThe Gardner threshold: a border between two glasses
https://services.math.duke.edu/mcal?abstract-9427
Glasses (aka amorphous solids) exhibit various anomalies when compared with
crystals (aka ordered solids), for instance, they display enhanced
transport, activated slow dynamics across energy barriers, excess
vibrational modes with respect to Debye's theory (the so-called Boson Peak)
or respond drastically to very small mechanical deformations. In this work,
we identify the common, universal origin to these anomalies in a realistic,
three-dimensional model of glasses. We show that in highly packed hard
spheres, vibrations become highly correlated in space and time at a sharply
defined threshold, which we call the "Gardner threshold". This work is
deeply related with the last developments in the analytical theory of
glasses, where the glass problem has been finally solved exactly in the
artificial limit of infinite spatial dimensions. The analytical solution
predicts the existence of a genuine phase transition (a Gardner phase
transition) within the glass, separating the glass and the jamming
transitions. In this work we, not only establish the relevance of the
(remanent of the) Gardner transition for real glasses, but also
characterize it using well-defined observables, including time-dependent
quantities and spatial correlations, that should be experimentally
measurable. See <a href="http://arxiv.org/abs/1511.04201"
>arxiv.org/abs/1511.04201</a><a href="https://scholar.google.com/citations?user=RyCweLUAAAAJ&hl=en">Beatriz Seoane</a> (ENS)2016-02-04T15:00:00-05:009427CNCSCNCS SeminarThursday, February 4, 2016, 3:00pmSpring, 2016Thu, 04 Feb 2016 16:00:00 EST119 PhysicsThu, 04 Feb 2016 15:00:00 ESTSocial contact processes and the partner model.
https://services.math.duke.edu/mcal?abstract-9407
We consider a model of infection spread on the complete graph on <I>N</I> vertices. Edges are dynamic, modelling the formation and breakup of non-permanent monogamous partnerships, and the infection can spread only along active edges. We identify a basic reproduction number \(R_0\) such that the infection dies off in \(O(\log N)\) time when \(R_0\)<1, and survives for at least \(e^{cN}\) time when \(R_0\)>1 and a positive fraction of vertices are initially infectious. We also identify a unique endemic state that exists when \(R_0\)>1, and show it is metastable. When \(R_0\)=1, with considerably more effort we can show the infection survives on the order of \(N^{1/2}\) amount of time.Eric Foxall (Arizona State U)2016-02-04T16:30:00-05:009407probabilityProbability Seminar119 PhysicsThu, 04 Feb 2016 16:30:00 ESTThursday, February 4, 2016, 4:30pmThu, 04 Feb 2016 17:30:00 ESTSpring, 2016Stochastic evolutionary modeling of cancer development and resistance to treatment
https://services.math.duke.edu/mcal?abstract-9464
Cancer is the result of a stochastic evolutionary process characterized by the accumulation of mutations that are responsible for tumor growth, immune escape, and drug resistance, as well as mutations with no effect on the phenotype. Stochastic modeling can be used to describe the dynamics of tumor cell populations and obtain insights into the hidden evolutionary processes leading to cancer. I will present recent approaches that use branching process models of cancer evolution to quantify intra-tumor heterogeneity and the development of drug resistance, and their implications for interpretation of cancer sequencing data and the design of optimal treatment strategies.<a href="http://ivanabozic.com/">Ivana Bozic</a> (Harvard and the Program for Evolutionary Dynamics)2016-02-05T12:00:00-05:009464mathematical biologyMathematical Biology Seminar130 PhysicsFri, 05 Feb 2016 12:00:00 ESTFriday, February 5, 2016, 12:00pmFri, 05 Feb 2016 13:00:00 ESTSpring, 2016Unraveling Kidney Physiology, Pathophysiology and Therapeutics: A Modeling Approach
https://services.math.duke.edu/mcal?abstract-9434
The kidney not only filters metabolic wastes and toxins from the body,
but it also regulates the body's water balance, electrolyte balance, and
acid-base balance, blood pressure, and blood flow. Despite intense
research, aspects of kidney functions remain incompletely understood. I
will discuss how our group use mathematical modeling techniques to
address a host of previously unanswered questions in renal physiology
and pathophysiology: Why is the mammalian kidney so susceptible to
hypoxia, despite receiving ~25% of the cardiac output? What are the
mechanisms underlying the development of acute kidney injury in a
patient who has undergone cardiac surgery performed on cardiopulmonary
bypass? What is the effect of inhibiting sodium-glucose transport, a
novel treatment for reducing renal glucose update in diabetes, on renal
NaCl transport and oxygen consumption?<a href="http://www.math.duke.edu/~alayton">Anita Layton</a> (Duke University)2016-02-08T12:00:00-05:009434Graduate-FacultyGraduate/faculty Seminar119 PhysicsMon, 08 Feb 2016 12:00:00 ESTMonday, February 8, 2016, 12:00pmSpring, 2016Mon, 08 Feb 2016 13:00:00 ESTPhysical Laws of Nature vs Fundamental First Principles
https://services.math.duke.edu/mcal?abstract-9384
In this talk, we attempt to derive some experimentally verifiable physical laws of nature based only on a few fundamental first principles. First, we present two basic principles, the principle of interaction dynamics (PID) and the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action under energy-momentum conservation constraint. PID offers a completely different and natural way of introducing Higgs fields. For gravity, we show that PID is the direct consequence of Einsteins principle of general relativity and the presence of dark matter and dark energy. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). PRI has remarkably rich physical consequences.
Second, we show that the physical laws of the four fundamental forcesgravity, electromagnetic force, weak and strong forcesare dictated by 1) the Einstein principle of general relativity, 2) the principle of gauge symmetry, 3) PID, and 4) PRI. The new theory will lead to solutions to a number of longstanding problems in particle physics and cosmology. The talk is based on recent joint work with Tian Ma.Shouhong Wang (Indiana University)2016-02-08T16:30:00-05:009384applied math and analysisApplied Math And Analysis SeminarSpring, 2016Mon, 08 Feb 2016 17:30:00 ESTMonday, February 8, 2016, 4:30pmMon, 08 Feb 2016 16:30:00 EST119 PhysicsThe distribution of points on cyclic l-covers of genus g
https://services.math.duke.edu/mcal?abstract-9280
We give an overview of a general trend of results that say that the distribution of the number of F_q-points of certain families of curves of genus g is asymptotically given by a sum of q+1 independent, identically distributed random variables as g goes to infinity. In particular, we discuss the distribution of the number of F_q-points for cyclic l-covers of genus g. (This is joint work with Bucur, David, Feigon, Kaplan, Ozman, Wood.) This work generalizes previous results in which only connected components of the moduli space were considered.<a href="http://www.dms.umontreal.ca/~mlalin/">Matilde Lalin</a> (Universite de Montreal)2016-02-10T13:30:00-05:009280Number TheoryNumber Theory SeminarWed, 10 Feb 2016 13:30:00 EST119 PhysicsWed, 10 Feb 2016 14:30:00 ESTSpring, 2016Wednesday, February 10, 2016, 1:30pmTraces of high powers of Frobenius for cubic covers of the projective line over finite fields
https://services.math.duke.edu/mcal?abstract-9498
The zeta function of a curve C over a finite field can be expressed in terms of the characteristic polynomial of its Frobenius endomorphism. We will see how one can compute the trace of high powers of this endomorphism in various moduli spaces. Finally, we will discuss how one can use this information to compute the one-level density -- which concerns low-lying zeros of the zeta function -- in the case of cubic covers of the projective line.Alina Bucur (UCSD)2016-02-10T16:30:00-05:009498Number TheoryNumber Theory SeminarWed, 10 Feb 2016 16:30:00 EST119 PhysicsSpring, 2016Wed, 10 Feb 2016 17:30:00 ESTWednesday, February 10, 2016, 4:30pmBlow up solutions and stability of peakons to integrable equations with nonlinear dispersion
https://services.math.duke.edu/mcal?abstract-9448
In this talk, we study blow-up mechanism of solutions to an integrable equation with cubic nonlinearities and nonlinear dispersion. We will show that singularities of the solutions can occur only in the form of wave-breaking. Some wave-breaking conditons on the initial data are provided. In addition, this equation is known to admit single and multi-peaked solitons, of a different character than those of the Camassa-Holm equation. We will prove that the shapes of these waves are stable under small perturbations in the energy space.Changzheng Qu (Northwest University, Xian, China)2016-02-11T10:00:00-05:009448applied math and analysisSpecial Talk Applied Math And Analysis SeminarThu, 11 Feb 2016 11:30:00 ESTSpring, 2016Thursday, February 11, 2016, 10:00amThu, 11 Feb 2016 10:00:00 ESTPhysics 119The Exciting Multicultural World of Mobile Tech, Content & Data Science
https://services.math.duke.edu/mcal?abstract-9493
In this talk, I will explore the intersection of mobile user growth patterns, content creation, mobile app creation, and data science. Please come hear about the ways in which data science and product design affect how well we experience the full spectrum of diverse, multicultural content on our mobile devices.Winston Henderson (Sankofa, Inc.)2016-02-11T11:45:00-05:009493Data DialogueData DialogueGross 330Thu, 11 Feb 2016 11:45:00 ESTThursday, February 11, 2016, 11:45amThu, 11 Feb 2016 12:45:00 ESTSpring, 2016A macroscopic multifractal analysis of parabolic stochastic PDEs
https://services.math.duke.edu/mcal?abstract-9399
We will show that the solutions to a large family of stochastic PDEs that behave as
the linear heat equation develop large-scale space-time peaks on infinitely-many different scales.
We formalize this assertion by appealing to the Barlow-Taylor theory of macroscopic fractals.
We will also present some earlier work on fixed-time results for comparison purposes.
This talk is based on a paper and a work in progress with Kunwoo Kim (Technion) and Yimin Xiao (Michigan State University).<a href="http://www.math.utah.edu/~davar/">Davar Khoshnevisan</a> (University of Utah)2016-02-11T16:30:00-05:009399probabilityProbability SeminarThu, 11 Feb 2016 17:30:00 ESTSpring, 2016Thursday, February 11, 2016, 4:30pmThu, 11 Feb 2016 16:30:00 EST119 PhysicsHierarchical population structure in blood diseases and cancer
https://services.math.duke.edu/mcal?abstract-9466
<a href="http://michorlab.dfci.harvard.edu/index.php/people/philipp-altrock">Philipp Altrock</a> (Dana Farber Cancer Institute)2016-02-12T12:00:00-05:009466mathematical biologyMathematical Biology SeminarSpring, 2016Fri, 12 Feb 2016 13:00:00 ESTFriday, February 12, 2016, 12:00pmFri, 12 Feb 2016 12:00:00 EST119 PhysicsCANCELLED; RESCHEDULED to Tuesday 3pm; Biomimetic 4D Printing
https://services.math.duke.edu/mcal?abstract-9515
The nascent technique of 4D printing has the potential to revolutionize manufacturing in fields ranging from organs-on-a-chip to architecture to soft robotics. By expanding the pallet of 3D printable materials to include the use stimuli responsive inks, 4D printing promises precise control over patterned shape transformations. With the goal of creating a new manufacturing technique, we have recently introduced a biomimetic printing platform that enables the direct control of local anisotropy into both the elastic moduli and the swelling response of the ink.
<br/>
<br/>
We have drawn inspiration from nastic plant movements to design a phytomimetic ink and printing process that enables patterned dynamic shape change upon exposure to water, and possibly other external stimuli. Our novel fiber-reinforced hydrogel ink enables local control over anisotropies not only in the elastic moduli, but more importantly in the swelling. Upon hydration, the hydrogel changes shape accord- ing the arbitrarily complex microstructure imparted during the printing process.
<br/>
<br/>
To use this process as a design tool, we must solve the inverse problem of prescribing the pattern of anisotropies required to generate a given curved target structure. We show how to do this by constructing a theory of anisotropic plates and shells that can respond to local metric changes induced by anisotropic swelling. A series of experiments corroborate our model by producing a range of target shapes inspired by the morphological diversity of flower petals.Elisabetta Matsumoto (Harvard University)2016-02-15T12:00:00-05:009515applied math and analysisApplied Math And Analysis SeminarSchiciano Auditorium, Side B, in CIEMAS/PrattMon, 15 Feb 2016 12:00:00 ESTMonday, February 15, 2016, 12:00pmMon, 15 Feb 2016 13:00:00 ESTSpring, 2016Parallel Computing Issues in Computational Chemistry
https://services.math.duke.edu/mcal?abstract-9386
In computational mathematics and science, it is now essential to consider computer hardware issues if a new algorithm is to be deployed. One such issue is the prevalence of parallelism in almost all levels of computer hardware. We discuss some of the challenges presented by computer hardware and some potential solutions in the context on quantum chemistry algorithms. Important considerations include reducing data movement, load balance across processors, and use of SIMD (single instruction, multiple data) features in modern processors. Specific results we have obtained include efficient computations using Hartree--Fock approximations on more than 1.5 million processor cores, and a new library for computing electron repulsion integrals that is designed for SIMD operation. These results are joint work with Ben Pritchard, Xing Liu, and the Intel Parallel Computing Lab.Edmond Chow (Georgia Institute of Technology)2016-02-15T16:30:00-05:009386applied math and analysisApplied Math And Analysis SeminarMon, 15 Feb 2016 16:30:00 EST119 PhysicsSpring, 2016Mon, 15 Feb 2016 17:30:00 ESTMonday, February 15, 2016, 4:30pmBiomimetic 4D Printing
https://services.math.duke.edu/mcal?abstract-9523
The nascent technique of 4D printing has the potential to revolutionize manufacturing in fields ranging from organs-on-a-chip to architecture to soft robotics. By expanding the pallet of 3D printable materials to include the use stimuli responsive inks, 4D printing promises precise control over patterned shape transformations. With the goal of creating a new manufacturing technique, we have recently introduced a biomimetic printing platform that enables the direct control of local anisotropy into both the elastic moduli and the swelling response of the ink.
<br/>
<br/>
We have drawn inspiration from nastic plant movements to design a phytomimetic ink and printing process that enables patterned dynamic shape change upon exposure to water, and possibly other external stimuli. Our novel fiber-reinforced hydrogel ink enables local control over anisotropies not only in the elastic moduli, but more importantly in the swelling. Upon hydration, the hydrogel changes shape accord- ing the arbitrarily complex microstructure imparted during the printing process.
<br/>
<br/>
To use this process as a design tool, we must solve the inverse problem of prescribing the pattern of anisotropies required to generate a given curved target structure. We show how to do this by constructing a theory of anisotropic plates and shells that can respond to local metric changes induced by anisotropic swelling. A series of experiments corroborate our model by producing a range of target shapes inspired by the morphological diversity of flower petals.Elisabetta Matsumoto (Harvard University)2016-02-16T15:00:00-05:009523applied math and analysisApplied Math And Analysis SeminarTue, 16 Feb 2016 15:00:00 ESTPhysics 119Spring, 2016Tue, 16 Feb 2016 16:00:00 ESTTuesday, February 16, 2016, 3:00pmRiemann-Hilbert problem for period integrals
https://services.math.duke.edu/mcal?abstract-9282
Period integrals of an algebraic variety are transcendental objects that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.<a href="http://people.brandeis.edu/~lian/">Bong H. Lian</a> (Brandeis University)2016-02-16T16:30:00-05:009282geometry/topologyGeometry/topology SeminarTue, 16 Feb 2016 16:30:00 EST119 PhysicsSpring, 2016Tue, 16 Feb 2016 17:30:00 ESTTuesday, February 16, 2016, 4:30pmFoodLogiQ, Connecting the World's Food Supply Chain
https://services.math.duke.edu/mcal?abstract-9513
Mr. Kennedy will focus on the forces driving the food industry to adopt sophisticated data collection tools and opportunities for big-data analysis using FoodLogiQ's cloud-based platform, <b>FoodLogiQ Connect</b> as an example.
<br>
About FoodLogiQ:
<br>
FoodLogiQ® LLC is a leading software as a service (SaaS) provider of traceability, food safety compliance and supply chain transparency software solutions. We help restaurant operators, food retailers and other food companies achieve end-to-end traceability while supporting safe and high quality food products across the supply chain. FoodLogiQ has a rapidly growing user base with over 2,0000 businesses in over 35 countries with 18,000 locations on our cloud platform. FoodLogiQ is located in the Research Triangle Park. www.foodlogiq.com<a href="https://www.foodlogiq.com/">Andy Kennedy</a> (FoodLogiQ)2016-02-18T11:45:00-05:009513Data DialogueData DialogueGross 330Thu, 18 Feb 2016 11:45:00 ESTThursday, February 18, 2016, 11:45amSpring, 2016Thu, 18 Feb 2016 12:45:00 ESTThe Parisi Formula: duality and equivalence of ensembles.
https://services.math.duke.edu/mcal?abstract-9401
In 1979, G. Parisi predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model and described the role played by its minimizer, called the Parisi measure. This remarkable formula was proven by Talagrand in 2006. In this talk I will explain a new representation of the Parisi functional that finally connects the temperature parameter and the Parisi measure as dual parameters.
Based on joint-works with Wei-Kuo Chen.<a href="http://math.northwestern.edu/~auffing/">Antonio Auffinger</a> (Northwestern University)2016-02-18T16:30:00-05:009401probabilityProbability SeminarThu, 18 Feb 2016 16:30:00 EST119 PhysicsSpring, 2016Thu, 18 Feb 2016 17:30:00 ESTThursday, February 18, 2016, 4:30pmAnalyzing Complex Systems and Networks: Incremental Optimization and Robustness
https://services.math.duke.edu/mcal?abstract-9521
Many of the emergent technologies and systems including infrastructure systems (communication, transportation and energy systems) and decision networks (sensor and robotic networks) require rapid processing of large data and comprise dynamic interactions that necessitate robustness to small errors, disturbances or outliers. <br/><br/>
Motivated by large-scale data processing in such systems, we first consider additive cost convex optimization problems (where each component function of the sum represents the loss associated to a data block) and propose and analyze novel incremental gradient algorithms which process component functions sequentially and one at a time, thus avoiding costly computation of a full gradient step. We focus on two randomized incremental methods, Stochastic Gradient Descent (SGD) and Random Reshuffling (RR), which have been the most widely used optimization methods in machine learning practice since the fifties. The only difference between these two methods is that RR samples the component functions without-replacement whereas SGD samples with-replacement. Much empirical evidence suggested that RR is faster than SGD, although no successful attempt has been made to explain and quantify this discrepancy for a long time. We provide the first theoretical convergence rate result of O(1/k^{2s}) for any s in (1/2,1) (and O(1/k^2) for a bias-removed novel variant) with probability one for RR showing its improvement over Ω(1/k) rate of SGD and highlighting the mechanism for this improvement. Our result relies on a detailed analysis of deterministic incremental methods and a careful study of random gradient errors. We then consider deterministic incremental gradient methods with memory and show that they can achieve a much-improved linear rate using a delayed dynamical system analysis. <br/><br/>
In the second part, we focus on large-scale continuous-time and discrete-time linear dynamical systems that model various interactions over complex networks and systems. There are a number of different metrics that can be used to quantify the robustness of such dynamical systems with respect to input disturbance, noise or error. Some key metrics are the H-infinity norm and the stability radius of the transfer matrix associated to the system. Algorithms to compute these metrics exist, but they are impractical for large-scale complex networks or systems where the dimension is large and they do not exploit the sparsity patterns in the network structure. We develop and analyze the convergence of a novel scalable algorithm to approximate both of the metrics for large-scale sparse networks. We then illustrate the performance of our method on numerical examples and discuss applications to design optimal control policies for dynamics over complex networks and systems.<a href="https://mert.lids.mit.edu/">Mert Gurbuzbalaban</a> (MIT)2016-02-19T12:00:00-05:009521applied math and analysisApplied Math And Analysis SeminarFri, 19 Feb 2016 12:00:00 ESTPhysics 130Fri, 19 Feb 2016 13:00:00 ESTSpring, 2016Friday, February 19, 2016, 12:00pmHow focused flexibility maximizes the thrust production of flapping wings
https://services.math.duke.edu/mcal?abstract-9468
Birds, insects, and fish all exploit the fact that flexible wings or fins generally perform better than their rigid counterparts. Given the task of designing an optimal wing, though, it is not clear how to best distribute the flexibility: Should the wing be uniformly flexible along its length, or could some advantage be gained by making certain sections more rigid than others? I will discuss this question by using a 2D small-amplitude model for the fluid-structure interaction combined with an efficient Chebyshev PDE solver. Numerical optimization shows that concentrating flexibility near the leading edge of the wing maximizes thrust production, an arrangement that resembles the torsional-joint flexibility mechanism found in insect wings. I will discuss the possibility of extending into three dimensions to address the question of optimal wing architecture more generally.<a href="http://www.math.fsu.edu/~moore/">Nick Moore</a> (Florida State)2016-02-19T16:30:00-05:009468mathematical biologyMathematical Biology SeminarSpring, 2016Fri, 19 Feb 2016 17:30:00 ESTFriday, February 19, 2016, 4:30pmFri, 19 Feb 2016 16:30:00 EST119 PhysicsMultiscale dynamics of dewetting fluid films
https://services.math.duke.edu/mcal?abstract-9439
Instabilities of thin liquid films spreading on solid surfaces are of
great interest for many applications involving coating flows and yield many
challenging mathematical problems.
Generally called "dewetting instabilities", several stages of dynamics
yield rupture, growth of dry spots, and ultimately break-up of the film
into sets of droplets. These instabilities can be represented in a
lubrication model consisting of a fourth-order nonlinear parabolic
PDE for the film height. The long-time behavior can be reduced to
a finite-dimensional dynamical system for the remaining droplets.
Mean field models can be constructed to describe the coarsening dynamics
for the number of droplets and
the distribution of drop sizes yielding macro-scale system properties
from the underlying small-scale nonlinear dynamics.<a href="http://www.math.duke.edu/~witelski/">Tom Witelski</a> (Duke University)2016-02-22T12:00:00-05:009439Graduate-FacultyGraduate/faculty SeminarPhysicsMon, 22 Feb 2016 12:00:00 ESTMonday, February 22, 2016, 12:00pmMon, 22 Feb 2016 13:00:00 ESTSpring, 2016Solving Equations using nonlinear approximations
https://services.math.duke.edu/mcal?abstract-9340
The idea of using nonlinear approximations as a tool for solving equations is as natural as that of using bases and, in fact, was proposed in 1960 in the context of quantum chemistry. The usual approach to solving partial differential and integral equations is to select a basis (possibly a multiresolution basis) or a grid, project equations onto such basis and solve the resulting discrete equations. The nonlinear alternative is to look for the solution within a large lass of functions (larger than
any basis) by constructing optimal or near optimal approximations at every step of an algorithm for solving the equations. While this approach can theoretically be very efficient, the difficulties of constructing optimal approximations prevented any significant use of it in practice.
However, during the last 15 years, nonlinear approximations have been successfully used to approximate operator kernels via exponentials or Gaussians to any user-specified accuracy, thus enabling a number of multidimensional multiresolution algorithms. In a new development several years ago, we constructed a fast and accurate reduction algorithm for optimal approximation of functions via exponentials or Gaussians (or, in a dual form, by rational functions) than can be used for solving partial differential and integral equations equations. We present two examples
of the resulting solvers: one for the viscous Burgers' equation and another for solving the Hartree-Fock equations of quantum chemistry. Burgers' equation is often used as a testbed for numerical methods: if the viscosity \vu; is small, its solutions develop sharp (moving) transition regions of width O (\vu) presenting significant challenges for numerical methods. Using nonlinear approximations for solving the Hartree-Fock equations is the first step to a wider use of the approach in quantum
chemistry. We maintain a functional form for the spatial orbitals as a linear combinations of products of decaying exponentials and spherical harmonics entered at the nuclear cusps. While such representations are similar to the classial Slater-type orbitals, in the course of computation we optimize both the exponents and the coefficients in order to achieve an efficient representation of solutions and to obtain guaranteed error bounds.Gregory Beylkin (University of Colorado Boulder)2016-02-22T16:30:00-05:009340applied math and analysisApplied Math And Analysis SeminarMonday, February 22, 2016, 4:30pmMon, 22 Feb 2016 17:30:00 ESTSpring, 2016119 PhysicsMon, 22 Feb 2016 16:30:00 ESTPhase retrieval in the setting of (semi-)continuous frames
https://services.math.duke.edu/mcal?abstract-9528
In this talk we first consider the following problem of phase retrieval in L2: Given a collection of real-valued bandlimited functions that constitutes a semi-discrete frame, we ask whether any real-valued function f can be uniquely recovered from the magnitudes of its convolutions with the frame elements. We find that under some mild assumptions this is indeed the case. Furthermore, it suffices to know the unsigned measurements on suitably fine lattices to uniquely determine f (up to a global sign factor).
In the second half of the talk we present a generalized framework for phase retrieval in Banach spaces and for measurements from continuous frames. Our main result states that when the Banach space is infinite dimensional, phase retrieval is unstable even for continuous frames. Therefore, in the setting of a discrete frame, no oversampling of the frame can improve on the stability of the phase retrieval problem.<a href="http://www.alaifari.com/">Rima Alaifari</a> (ETH Zurich)2016-02-25T11:45:00-05:009528Data DialogueData DialogueThursday, February 25, 2016, 11:45amThu, 25 Feb 2016 12:45:00 ESTSpring, 2016Gross 330Thu, 25 Feb 2016 11:45:00 ESTStochastic approach to anomalous diffusion in two dimensional, incompressible, periodic, cellular flows.
https://services.math.duke.edu/mcal?abstract-9317
It is a well known fact that velocity grandients in a flow change the dispersion of a passive tracer. One clear manifestation of this phenomenon is that in systems with homogenization type diffusive long time/large scale behavior, the effective diffusivity often differs greatly from the molecular one. An important aspect of these well known result is that they are only valid on timescales much longer than the inverse diffusivity. We are interested in what happens on shorter timescales (subhomogenization regimes) in a family of two-dimensional incompressible periodic flows that consists only of pockets of recirculations essentially acting as traps and infinite flowlines separating these where significant transport is possible. Our approach is to follow the random motion of a tracer particle and show that under certain scaling it resembles time-changed Brownian motions. This shows that while the trajectories are still diffusive, the variance grows differently than linear.<a href="http://math.nyu.edu/~zsolt/">Zsolt Pajor-Gyulai</a> (Courant Institute - NYU)2016-02-25T16:30:00-05:009317probabilityProbability SeminarSpring, 2016Thu, 25 Feb 2016 17:30:00 ESTThursday, February 25, 2016, 4:30pmThu, 25 Feb 2016 16:30:00 EST119 PhysicsForecasting and uncertainty in modeling disease dynamics
https://services.math.duke.edu/mcal?abstract-9470
Connecting dynamic models with data to yield predictive results
often requires a variety of parameter estimation, identifiability, and
uncertainty quantification techniques. These approaches can help to determine what is possible to estimate from a given model and data set, and help guide new data collection. Here, we examine how parameter estimation and disease forecasting are affected when examining disease transmission via multiple types or pathways of transmission. Using examples taken from the West Africa Ebola epidemic, HPV, and cholera, we illustrate some of the potential difficulties in estimating the
relative contributions of different transmission pathways, and show how
alternative data collection may help resolve this unidentifiability. We
also illustrate how even in the presence of large uncertainties in the data and model parameters, it may still be possible to successfully forecast disease dynamics.<a href="https://sph.umich.edu/faculty-profiles/eisenberg-marisa.html">Marisa Eisenberg</a> (Michigan)2016-02-26T12:00:00-05:009470mathematical biologyMathematical Biology SeminarFriday, February 26, 2016, 12:00pmFri, 26 Feb 2016 13:00:00 ESTSpring, 2016119 PhysicsFri, 26 Feb 2016 12:00:00 ESTThe augmentation category map induced by exact Lagrangian cobordisms
https://services.math.duke.edu/mcal?abstract-9430
To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two ends. We study the functor and establish a long exact sequence relating the corresponding Legendrian cohomology categories of the two ends. As applications, we prove that the functor between augmentation categories is injective on objects, and find new obstructions to the existence of exact Lagrangian cobordisms. The main technique is a recent work of Chantraine, Dimitroglou Rizell, Ghiggini and Golovko on Cthulhu homology.<a href="https://sites.google.com/site/yupanduke/">Yu Pan</a> (Duke University)2016-02-29T12:00:00-05:009430Graduate-FacultyGraduate/faculty SeminarMonday, February 29, 2016, 12:00pmMon, 29 Feb 2016 13:00:00 ESTSpring, 2016119 PhysicsMon, 29 Feb 2016 12:00:00 ESTOn two dimensional gravity water waves with angled crests
https://services.math.duke.edu/mcal?abstract-9342
In this talk, I will survey the recent understandings on the motion of water waves obtained via rigorous
mathematical tools, this includes the evolution of smooth initial data and some typical singular
behaviors. In particular, I will present our recently results on gravity water waves with angled crests.Sijue Wu (University of Michigan)2016-02-29T16:30:00-05:009342applied math and analysisApplied Math And Analysis SeminarMon, 29 Feb 2016 16:30:00 EST119 PhysicsMon, 29 Feb 2016 17:30:00 ESTSpring, 2016Monday, February 29, 2016, 4:30pmQ: How many folded angels can dance on the head of pin? A: 22+/-5
https://services.math.duke.edu/mcal?abstract-9420
For centuries, origami, the Japanese art of paper folding, has been a
powerful technique for transforming two dimensional sheets into beautiful
three dimensional sculptures. Recently, origami has made its foray into a
new realm, that of physics and engineering, where it has been
revolutionizing our concept of materials design. In this talk I will
describe the new design principles we are uncovering for determining the
shape, mechanics, and transformations of origami structures along with their usefulness in areas as diverse as solar sail design, architecture, and even fashion.
Arguably however, the greatest strength of this new paradigm is the fact
that origami is intrinsically scalable. Thus sculptures built at one size
can be shrunk down smaller and smaller. This begs the question: what is the smallest fold one can make? Or in other words, how many folded angels can dance on the head of a pin? The rest of this talk will take a deep dive into how origami has been marching smaller and smaller in size. From folding by hand, to self-folding through shape memory alloys and even
folding via polymer layers, I will argue that the ultimate limit for scaling down origami is set by folding a sheet of atomic dimensions. I will conclude by showing this vision: realized in
the folds of a single sheet of graphene.<a href="http://www.physics.cornell.edu/professorspeople/professors/?page=website/faculty&action=show/id=7">Itai Cohen</a> (Dept of Physics, Cornell)2016-03-01T15:00:00-05:009420CNCSCNCS SeminarTuesday, March 1, 2016, 3:00pmTue, 01 Mar 2016 16:00:00 ESTSpring, 2016119 PhysicsTue, 01 Mar 2016 15:00:00 ESTA tale of two norms.
https://services.math.duke.edu/mcal?abstract-9379
The first cohomology of a hyperbolic 3-manifold has two natural norms:
the Thurston norm, which measure topological complexity of surfaces
representing the dual homology class, and the harmonic norm, which is
just the L^2 norm on the corresponding space of harmonic 1-forms.
Bergeron-Sengun-Venkatesh recently showed that these two norms are
closely related, at least when the injectivity radius is bounded below.
Their work was motivated by the connection of the harmonic norm to the
Ray-Singer analytic torsion and issues of torsion growth. After carefully introducing both norms and the
connection to torsion growth, I will discuss new results that refine and
clarify the precise relationship between them; one tool here will be a
third norm based on least-area surfaces. This is joint work with Jeff
Brock.<a href="http://www.math.uiuc.edu/~nmd/">Nathan Dunfield</a> (University of Illinois at Urbana-Champaign)2016-03-01T16:30:00-05:009379geometry/topologyGeometry/topology SeminarTue, 01 Mar 2016 17:30:00 ESTSpring, 2016Tuesday, March 1, 2016, 4:30pmTue, 01 Mar 2016 16:30:00 EST119 PhysicsElliptic curves over $\mathbb{Q}$ and 2-adic images of Galois
https://services.math.duke.edu/mcal?abstract-9318
Given an elliptic curve $E/\mathbb{Q}$, let $E[2^k]$ denote the set of points on $E$ that have order dividing $2^k$. The coordinates of these points are algebraic numbers and using them, one can build a Galois representation $\rho : G_{\mathbb{Q}} \to \GL_{2}(\mathbb{Z}_{2})$.
We give a classification of all possible images of this Galois representation. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.Jeremy Rouse (Wake Forest University)2016-03-02T13:30:00-05:009318Number TheoryNumber Theory SeminarSpring, 2016Wed, 02 Mar 2016 14:30:00 ESTWednesday, March 2, 2016, 1:30pmWed, 02 Mar 2016 13:30:00 EST119 PhysicsSingularities of formal arc spaces of reductive monoids
https://services.math.duke.edu/mcal?abstract-9526
I will discuss the relation between singularities in formal arc spaces of certain reductive monoids and local factors of automorphic L-functions.Ngo, Bau Chau 2016-03-02T16:30:00-05:009526Number TheoryNumber Theory SeminarWed, 02 Mar 2016 17:30:00 ESTSpring, 2016Wednesday, March 2, 2016, 4:30pmWed, 02 Mar 2016 16:30:00 EST119 PhysicsCutoff for the noisy voter model
https://services.math.duke.edu/mcal?abstract-9408
Given a continuous time Markov Chain \( q(x,y)\) on a
finite set <I>S</I>, the associated noisy voter model is the
continuous time Markov chain on \(\{0,1\}^S\) which evolves
by (i) for each two sites x and y in <I>S</I>, the state at
site x changes to the value of the state at site
y at rate \( q(x,y) \) and (ii) each site rerandomizes
its state at rate 1. We show that if there is a uniform
bound on the rates \(q(x,y)\) and the corresponding
stationary distributions are ``almost'' uniform, then the
mixing time has a sharp cutoff at time \(\log |S|/2\) with a
window of order 1. Lubetzky and Sly proved cutoff with a
window of order 1 for the stochastic Ising model on
toroids: we obtain the special case of their result for
the cycle as a consequence of our result.Ted Cox (Syracuse)2016-03-03T16:30:00-05:009408probabilityProbability SeminarThursday, March 3, 2016, 4:30pmSpring, 2016Thu, 03 Mar 2016 17:30:00 EST119 PhysicsThu, 03 Mar 2016 16:30:00 ESTStochastic Models of Protein Evolution
https://services.math.duke.edu/mcal?abstract-9472
Stochastic evolutionary models of biological sequences are widely used for phylogenetic inference and ancestral reconstruction. However, at long divergence times sequences enter the "twilight zone" of homology detection and reconstruction becomes very difficult. We describe a stochastic evolutionary model for protein 3D structure using elements of shape theory. This model significantly resolves this uncertainty and stabilizes evolutionary inferences. We also provide theoretical bounds on inferring evolutionary divergence times via connections to the probabilistic "cutoff phenomenon", in which a Markov chain remains far equilibrium for an extended period followed by a rapid transition into equilibrium. We show that this cutoff explains several previously reported problems with common default priors for Bayesian phylogenetic analysis, and suggest a new class of priors to address these problems.<a href="http://www2.stat.duke.edu/~scs/Students.shtml">Scott Schmidler</a> (Duke statistics)2016-03-04T12:00:00-05:009472mathematical biologyMathematical Biology SeminarSpring, 2016Fri, 04 Mar 2016 13:00:00 ESTFriday, March 4, 2016, 12:00pmFri, 04 Mar 2016 12:00:00 EST119 PhysicsFirst-time thin film rupture driven by generalized evaporative loss
https://services.math.duke.edu/mcal?abstract-9433
Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. This talk will focus on the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term due to evaporation. Several different types of finite-time singularities are observed due to balances between evaporation and surface tension or intermolecular forces. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.<a href="https://fds.duke.edu/db/aas/math/grad/hangjie.ji">Hangjie Ji</a> (Duke University)2016-03-07T12:00:00-05:009433Graduate-FacultyGraduate/faculty SeminarMonday, March 7, 2016, 12:00pmMon, 07 Mar 2016 13:00:00 ESTSpring, 2016LoungeMon, 07 Mar 2016 12:00:00 ESTPhase Retreival: From Convex to Nonconvex Methods
https://services.math.duke.edu/mcal?abstract-9344
In phase retrieval, one aims to recover a signal from magnitude measurements. In the literature, an effective SDP algorithm, referred to as PhaseLift, was proposed with numerical success as well as strong theoretical guarantees. In this talk, I will first introduce some recent theoretical developments for PhaseLift, which demonstrate the applicability and adaptivity of this convex method.
Although convex methods are provably effective and robust, the computational complexity may be relatively high. Moreover, there is often an issue of storage to solve the lifted problem. To address these issues, we introduce a nonconvex optimization algorithm, named Wirtinger flow, with theoretically guaranteed performance. It is much more efficient than convex methods in terms of computation and memory. Finally, I will introduce how to modify Wirtinger flow when the signal is known to be sparse, in order to improve the accuracy of the recovery.<a href="http://www.stat.ucdavis.edu/~xdgli/index.html">Xiaodong Li</a> (University of California Davis)2016-03-07T16:30:00-05:009344applied math and analysisApplied Math And Analysis SeminarMon, 07 Mar 2016 16:30:00 EST119 PhysicsMon, 07 Mar 2016 17:30:00 ESTSpring, 2016Monday, March 7, 2016, 4:30pmA glass transition in population genetics: Emergence of clones in populations
https://services.math.duke.edu/mcal?abstract-9422
The fields of evolution and population genetics are undergoing a
renaissance, due to the abundance of sequencing data. On the other hand, the
existing theories are often unable to explain the experimental findings. It
is not clear what sets the time scales of evolution, whether for antibiotic
resistance, an emergence of new animal species, or the diversification of
life. The emerging picture of genetic evolution is that of a strongly
interacting stochastic system with large numbers of components far from
equilibrium. In this talk, I plan to focus on the clone competition and
discuss the diversity of a random population that undergoes selection and
recombination (sexual reproduction). Recombination reshuffles genetic
material while selection amplifies the fittest genotypes. If recombination
is more rapid than selection, a population consists of a diverse mixture of
many genotypes, as is observed in many populations. In the opposite regime,
selection can amplify individual genotypes into large clones, and the
population reaches the so-called "clonal condensation". I hope to convince
you that our work provides a qualitative explanation of clonal condensation.
I will point out the similarity between clonal condensation and the freezing
transition in the Random Energy Model of spin glasses. I will conclude with
a summary of our present understanding of the clonal condensation phenomena
and describe future directions and connections to statistical physics.<a href="http://www.phys.virginia.edu/People/personal.asp?UID=mv8h">Marija Vucelja</a> (Dept of Physics, University of Virginia)2016-03-08T15:00:00-05:009422CNCSCNCS SeminarTuesday, March 8, 2016, 3:00pmSpring, 2016Tue, 08 Mar 2016 16:00:00 EST119 PhysicsTue, 08 Mar 2016 15:00:00 ESTPartial compactification and metric asymptotics of monopoles
https://services.math.duke.edu/mcal?abstract-9414
I will describe a partial compactification of the moduli space, M_k, of SU(2) magnetic monopoles on R^3, wherein monopoles of charge k decompose into widely separated `monopole clusters' of lower charge going off to infinity at comparable rates. The hyperkahler metric on M_k has a complete asymptotic expansion, the leading terms of which generalize the asymptotic metric discovered by Bielawski, Gibbons and Manton in the case that the monopoles are all widely separated. This is joint work with M. Singer, and is part of a larger work in progress with R. Melrose and K. Fritzsch to fully compactify the M_k as manifolds with corners and determine their L^2 cohomology.<a href="http://www.northeastern.edu/ckottke/">Chris Kottke</a> (Northeastern University)2016-03-08T16:30:00-05:009414geometry/topologyGeometry/topology SeminarTue, 08 Mar 2016 16:30:00 EST119 PhysicsSpring, 2016Tue, 08 Mar 2016 17:30:00 ESTTuesday, March 8, 2016, 4:30pmUnified Theory of Inertial Granular Flows and Non-Brownian Suspensions
https://services.math.duke.edu/mcal?abstract-9551
The rheology of dense flows of hard particles is singular near the jamming
threshold where flow ceases, both for aerial granular flows dominated by
inertia, and for over-damped suspensions. At the same time, the length
scale characterizing velocity correlations appears to diverge at jamming.
We introduce a theoretical framework that proposes a potentially complete
scaling description of stationary flows of frictionless particles. We
compare our predictions with the empirical literature, as well as with new
numerical data. Overall we find a very good agreement between theory and
observations. Finally, we use simulations of frictional inertial flow to
outline the regime of the phase diagram where the theory holds, and show
where friction adds new physics.<a href="https://people.epfl.ch/eric.degiuli?lang=en">Eric DeGiuli</a> (EPF Lausanne)2016-03-10T15:00:00-05:009551CNCSCNCS SeminarThu, 10 Mar 2016 16:00:00 ESTSpring, 2016Thursday, March 10, 2016, 3:00pmThu, 10 Mar 2016 15:00:00 EST119 PhysicsMean Field Games: theory and applications
https://services.math.duke.edu/mcal?abstract-9405
We review the Mean Field Game (MFG) paradigm introduced independently by Caines-Huang-Malhame and Lasry Lyons ten years ago, and we illustrate the relevance for applications with a couple of examples (bird flocking and room exit). We then review the probabilistic approach based on Forward-Backward Stochastic Differential Equations (FBSDEs), and we derive the Master Equation from a version of the chain rule (Ito's formula) for functions over flows of probability measures. Finally, we give a new form to the extension of MFGs to the case of major and minor players and, at least in the finite state space case, we describe an application to virus contagion (e.g. cyber security).<a href="https://www.princeton.edu/~rcarmona/">Rene Carmona</a> (Princeton University)2016-03-10T16:30:00-05:009405probabilityProbability SeminarThu, 10 Mar 2016 16:30:00 EST119 PhysicsThu, 10 Mar 2016 17:30:00 ESTSpring, 2016Thursday, March 10, 2016, 4:30pmno talk
https://services.math.duke.edu/mcal?abstract-9474
Friday is the start of spring break 2016-03-11T12:00:00-05:009474mathematical biologyMathematical Biology SeminarFriday, March 11, 2016, 12:00pmFri, 11 Mar 2016 13:00:00 ESTSpring, 2016119 PhysicsFri, 11 Mar 2016 12:00:00 ESTVisualising the arithmetic of imaginary quadratic fields
https://services.math.duke.edu/mcal?abstract-9517
Let $K$ be an imaginary quadratic field with ring of integers $\mathcal{O}_K$. The Schmidt arrangement of $K$ is the orbit of the extended real line in the extended complex plane under the Mobius transformation action of the Bianchi group $\operatorname{PSL}(2,\mathcal{O}_K)$. The arrangement takes the form of a dense collection of intricately nested circles. Aspects of the number theory of $\mathcal{O}_K$ can be characterised by properties of this picture: for example, the arrangement is connected if and only if $\mathcal{O}_K$ is Euclidean. I'll explore this structure and its connection to Apollonian circle packings. Specifically, the Schmidt arrangement for the Gaussian integers is a disjoint union of all primitive integral Apollonian circle packings. Generalizing this relationship to all imaginary quadratic $K$, the geometry naturally defines some new circle packings and thin groups of arithmetic interest.Kate Stange (UC Boulder)2016-03-16T16:30:00-04:009517Number TheoryNumber Theory SeminarWed, 16 Mar 2016 16:30:00 EDT119 PhysicsWed, 16 Mar 2016 17:30:00 EDTSpring, 2016Wednesday, March 16, 2016, 4:30pmno talk
https://services.math.duke.edu/mcal?abstract-9475
Spring Break 2016-03-18T12:00:00-04:009475mathematical biologyMathematical Biology Seminar119 PhysicsFri, 18 Mar 2016 12:00:00 EDTFriday, March 18, 2016, 12:00pmFri, 18 Mar 2016 13:00:00 EDTSpring, 2016Practical uses of Complex Analysis
https://services.math.duke.edu/mcal?abstract-9559
The notion of conformal mapping is of fundamental importance in complex analysis. Conformal maps are used by mathematicians, physicists and engineers to change regions with complicated shapes into much simpler ones, and to do so in a way that preserves shape on a small scale (that is, when viewed up close).
This makes it possible to ``transpose a problem that was formulated for the complicated-looking region into another, related problem for the simpler region(where it can be easily solved) -- then one uses conformal mapping to ``translate'' the solution of the problem over the simpler region, back to a solution of the original problem (over the complicated region).
The beauty of conformal mapping is that its governing principle is based on a very simple idea that is easy to explain and to understand (much like the statement of Fermat's celebrated last theorem) .
In the first part of this talk I will introduce the notion of conformal mapping and will briefly go over its basic properties and some of its history (including a historical mystery going back to Galileo Galilei). I will then describe some of the many real-life applications of conformal maps, including: cartography; airplane wing design (transonic flow); art (in particular, the so-called ``Droste effect in the work of M. C. Escher).
Time permitting, I will conclude by highlighting a 2013 paper by McArthur fellow L. Mahadevan that uses the related notion of quasi-conformal mapping to link D'Arcy Thompson's iconic work On Shape and Growth (published in 1917) with modern morphometric analysis (a discipline in biology that studies, among other things, how living organisms evolve over time).
No previous knowledge of complex analysis is needed to enjoy this talk.Loredana Lanzani (University of Syracuse)2016-03-21T12:00:00-04:009559Graduate-FacultyGraduate/faculty SeminarMon, 21 Mar 2016 12:00:00 EDT119 PhysicsSpring, 2016Mon, 21 Mar 2016 13:00:00 EDTMonday, March 21, 2016, 12:00pmHarmonic Analysis Techniques in Several Complex Variables
https://services.math.duke.edu/mcal?abstract-9346
This talk concerns recent joint work with E. M. Stein on the extension to higher dimension of Calder\'ons and Coifman-McIntosh-Meyers seminal results about the Cauchy integral for a Lipschitz planar curve (interpreted as the boundary of a Lipschitz domain $D\subset \mathbb{C}$). From the point of view of complex analysis, a fundamental feature of the 1-dimensional Cauchy kernel is that it is holomorphic (that is, analytic) as a function of $z \in D$. In great contrast with the one-dimensional theory, in higher dimension there is no obvious holomorphic analogue of $H(w, z)$. This is because of geometric obstructions (the Levi problem) that in dimension 1 are irrelevant.
A good candidate kernel for the higher dimensional setting was first identified by Jean Leray in the context of a $C^{\infty}$-smooth, convex domain $D$: while these conditions on $D$ can be relaxed a bit, if the domain is less than $C^2$-smooth (much less Lipschitz!) Lerays construction becomes conceptually problematic.
In this talk I will present (a), the construction of the Cauchy-Leray kernel and (b), the (b) the $L^p(bD)$-boundedness of the induced singular integral operator under the weakest currently known assumptions on the domains regularity in the case of a planar domain these are akin to Lipschitz boundary, but in our higher-dimensional context the assumptions we make are in fact optimal. The proofs rely in a fundamental way on a suitably adapted version of the so-called T(1)-theorem technique from real harmonic analysis.
Time permitting, I will describe applications of this work to complex function theory specifically, to the Szeg\"o and Bergman projections (that is, the orthogonal projections of $L^2$ onto, respectively, the Hardy and Bergman spaces of holomorphic functions).Loredana Lanzani (Syracus University)2016-03-21T15:00:00-04:009346applied math and analysisApplied Math And Analysis SeminarSpring, 2016Mon, 21 Mar 2016 16:00:00 EDTMonday, March 21, 2016, 3:00pmMon, 21 Mar 2016 15:00:00 EDTTBAPeriods, Galois theory and particle physics: General introduction to periods
https://services.math.duke.edu/mcal?abstract-9553
A period is a certain kind of complex number which can be written as an integral of algebraic quantities. Kontsevich and Zagier conjectured that all identities between periods can be obtained from the elementary rules of calculus. After discussing several examples I will focus on the case of multiple zeta values which were first introduced in a special case by Euler, and now occur in numerous branches of mathematics. They satisfy many families of relations which are the subject of several open conjectures.<a href="https://www.asc.ox.ac.uk/person/2245">Francis Brown</a> (All Souls College Oxford)2016-03-21T16:30:00-04:009553Gergen LecturesGergen Lectures SeminarSpring, 2016Mon, 21 Mar 2016 17:30:00 EDTMonday, March 21, 2016, 4:30pmMon, 21 Mar 2016 16:30:00 EDTPhysics 128Tensor networks for the real world
https://services.math.duke.edu/mcal?abstract-9352
I will provide a pedagogical introduction to the ideas of tensor networks, an efficient representation for high-dimensional objects, and their connection to renormalization group ideas. I will then discuss some examples of how they are impacting simulations of quantum mechanical systems in chemistry, physics, and materials.Garnet Chan (Princeton University)2016-03-22T11:40:00-04:009352CTMS Adventures in Theory LecturesCTMS Adventures In Theory Lectures SeminarFrench Family Science Center 2237Tue, 22 Mar 2016 11:40:00 EDTTuesday, March 22, 2016, 11:40amSpring, 2016Tue, 22 Mar 2016 13:00:00 EDTStabilization of the Khovanov Homotopy Type of Torus Links
https://services.math.duke.edu/mcal?abstract-9412
Both the Jones polynomial and its categorification, the Khovanov homology, are known to stabilize for torus links T(n,m) as m goes to infinity. In recent work, Robert Lipshitz and Sucharit Sarkar constructed the Khovanov homotopy type of a link, a spectrum whose reduced cohomology recovers the Khovanov homology of the link. In this talk I will discuss stability of these homotopy types for torus links as m goes to infinity. If time permits, I will also discuss more recent work regarding a tail as n to goes to infinity (similar to the tail of the colored Jones polynomial), as well as a definition for a colored Khovanov homotopy type for links.<a href="http://www.math.virginia.edu/people/msw3ka">Mike Willis</a> (University of Virginia)2016-03-22T12:00:00-04:009412geometry/topologyGeometry/topology SeminarTue, 22 Mar 2016 12:00:00 EDT205 PhysicsSpring, 2016Tue, 22 Mar 2016 13:00:00 EDTTuesday, March 22, 2016, 12:00pmPeriods, Galois theory and particle physics: Amplitudes in high-energy physics
https://services.math.duke.edu/mcal?abstract-9554
In high-energy physics, interactions between fundamental particles can be represented by Feynman graphs. Almost all predictions for particle collider experiments are obtained by computing certain integrals associated to such graphs, called Feynman integrals, and a vast effort in the physics community worldwide is devoted to studying these quantities. Feynman integrals turn out to be periods, and surprisingly many are multiple zeta values. I will survey what is known and not known about these quantities.<a href="https://www.asc.ox.ac.uk/person/2245">Francis Brown</a> (All Souls College Oxford)2016-03-22T16:30:00-04:009554Gergen LecturesGergen Lectures SeminarPhysics 119Tue, 22 Mar 2016 16:30:00 EDTTuesday, March 22, 2016, 4:30pmSpring, 2016Tue, 22 Mar 2016 17:30:00 EDTThe Equidistribution of Lattice Shapes of Rings of Integers in Cubic, Quartic, and Quintic Number Fields
https://services.math.duke.edu/mcal?abstract-9438
Piper Harron presents the delightfully mathematical one woman show that answers questions her audience may have never asked itself before now! Such as: What is the shape of a number field? And: How do we show shapes are equidistributed? She will sketch the proof, providing references to old stuff and details to new stuff. Come one, come all (people, especially graduate students, interested in number theory)!Piper Harron 2016-03-23T13:30:00-04:009438Number TheoryNumber Theory Seminar119 PhysicsWed, 23 Mar 2016 13:30:00 EDTWednesday, March 23, 2016, 1:30pmSpring, 2016Wed, 23 Mar 2016 14:30:00 EDTThe shapes of special families of number fields
https://services.math.duke.edu/mcal?abstract-9544
NOTE SPECIAL TIME AND LOCATION: 3:30 Gross Hall 330
As a sequel to the earlier talk of Piper Harron's discussing the equidistribution of shapes of S_n number fields of degree n, I will present results on the shapes of number fields living in less generic families. In particular, I will discuss shapes of number fields having non-trivial automorphisms, such as Galois quartics. Another type of family discussed will be cubic fields with fixed quadratic resolvent. All this will be included in a survey of what is known about shapes of number fields.Robert Harron 2016-03-23T15:30:00-04:009544Number TheoryNumber Theory SeminarSpring, 2016Wed, 23 Mar 2016 16:30:00 EDTWednesday, March 23, 2016, 3:30pmWed, 23 Mar 2016 15:30:00 EDTGross Hall 330Periods, Galois theory and particle physics: Galois theory and transcendence
https://services.math.duke.edu/mcal?abstract-9555
Classical Galois theory replaces the study of algebraic numbers with group theory. This idea is extremely powerful, and led to the proof of the insolubility of the general quintic equation. A deep idea,
originating in the work of Grothendieck, is that Galois theory should extend to the theory of periods. I will describe a cheap way to set up such a theory and illustrate it in the case of multiple zeta values.
It gives rise to a symmetry group which respects the algebraic identities satisfied by these numbers and explains their underlying structure.<a href="https://www.asc.ox.ac.uk/person/2245">Francis Brown</a> (All Souls College Oxford)2016-03-23T16:30:00-04:009555Gergen LecturesGergen Lectures SeminarWednesday, March 23, 2016, 4:30pmWed, 23 Mar 2016 17:30:00 EDTSpring, 2016Physics 119Wed, 23 Mar 2016 16:30:00 EDTMulti-scale simulation of crystal defects
https://services.math.duke.edu/mcal?abstract-9563
PART 1: I will construct a mathematical model of a defect embedded in an infinite homogeneous crystal. I will then establish a regularity result for minimisers, which given the crucial information on which approximation schemes are based. As an elementary application of this framework I will prove convergence rates for two computational schemes: (1) clamped far-field and (2) coupling to harmonic far-field model. <br/>
PART 2: The conditions under which the theory of Part 1 holds are separability and locality of the total energy. In Part 2 I will show how for a tight-binding model (a minimalistic electronic structure model) these two condition arise. This analysis raises some interesting (open) questions.<br/>
PART 3: Finally, I will use the theory developed in PART 1 and PART 2 to construct and analyse a new family of QM/MM embedding schemes with rigorous error estimates.<a href="http://homepages.warwick.ac.uk/staff/C.Ortner/">Christoph Ortner</a> (University of Warwick)2016-03-24T10:00:00-04:009563applied math and analysisApplied Math And Analysis SeminarThursday, March 24, 2016, 10:00amThu, 24 Mar 2016 11:00:00 EDTSpring, 2016119 PhysicsThu, 24 Mar 2016 10:00:00 EDTFrom Theory to Practice: Integrating Geometric and Topological Ideas into Real World Systems
https://services.math.duke.edu/mcal?abstract-9534
For many years there has been a lot of basic research on Shape Analysis as an approach to discovering
new relationships, dependencies, measurements and classifications from datasets in high dimensions. In
the last 15 years, applications of methods from Topology and Differential Geometry have been developed
for this purpose and integrated with statistical and machine learning approaches.
<p>
In this talk we will first give an introduction and overview for one example, namely Topological
Data Analysis, and discuss how it can be used to provide features for machine learning in a variety
of settings. Secondly, we will discuss the ongoing challenges of translating this method into actual
practice in these same settings. We hope this second half will give some insight into a basic challenge that
faces all university research: it's much harder to apply your exciting new ideas than you think - most of
the challenge is both how to prove its value and how to integrate it with what's already in use.<a href="http://www.geomdata.com">John Harer</a> (Geometric Data Analytics, Inc.)2016-03-24T11:45:00-04:009534Data DialogueData DialogueGross 330Thu, 24 Mar 2016 11:45:00 EDTThursday, March 24, 2016, 11:45amSpring, 2016Thu, 24 Mar 2016 12:45:00 EDTPeriods, Galois theory and particle physics: Applications
https://services.math.duke.edu/mcal?abstract-9556
In the final lecture, I will propose how the Galois theory of periods should lead to a classification of periods by types. When applied to the set of Feynman integrals occurring in particle physics, experiments suggest the emergence of a `cosmic? Galois group of symmetries acting on the constants of high-energy physics.<a href="https://www.asc.ox.ac.uk/person/2245">Francis Brown</a> (All Souls College Oxford)2016-03-24T16:30:00-04:009556Gergen LecturesGergen Lectures SeminarThu, 24 Mar 2016 17:30:00 EDTSpring, 2016Thursday, March 24, 2016, 4:30pmThu, 24 Mar 2016 16:30:00 EDTPhysics 119Taking a dip in the gene pool: Insights from pooled population sequencing
https://services.math.duke.edu/mcal?abstract-9247
Advances in high-throughput genomics have facilitated the development of pooled population sequencing techniques which involve the en masse sequencing of tens to hundreds of individual genomes in a single sequencing reaction. Pooled population sequencing methods have numerous applications in quantitative, population and evolutionary genetics. I will discuss some of the statistical and computational challenges associated with the analysis of pooled sequence data in the context of quantitative trait locus (QTL) mapping and detecting selection during experimental evolution.<a href="http://sites.biology.duke.edu/magwenelab/">Paul Magwene</a> (Duke University)2016-03-25T12:00:00-04:009247mathematical biologyMathematical Biology SeminarFri, 25 Mar 2016 12:00:00 EDT119 PhysicsFri, 25 Mar 2016 13:00:00 EDTSpring, 2016Friday, March 25, 2016, 12:00pmGrad Recruit Panel Discussions
https://services.math.duke.edu/mcal?abstract-9568
TBATBD 2016-03-25T13:30:00-04:009568Department of MathematicsOther Meetings and EventsGrad Recruit Panel DiscussionsSpring, 2016Fri, 25 Mar 2016 14:30:00 EDTFriday, March 25, 2016, 1:30pmFri, 25 Mar 2016 13:30:00 EDTPhysics 119Grad Recruitment
https://services.math.duke.edu/mcal?abstract-9569
TBAMath Slam 2016-03-25T16:30:00-04:009569Department of MathematicsMath SlamFriday, March 25, 2016, 4:30pmFri, 25 Mar 2016 17:30:00 EDTSpring, 2016Physics 119Fri, 25 Mar 2016 16:30:00 EDTUniqueness of photon spheres in static relativistic spacetimes
https://services.math.duke.edu/mcal?abstract-9500
The Schwarzschild spacetime models the exterior region of a spherically symmetric, static star or black hole in general relativity. It possesses a very special, timelike hypersurface which is ruled by and traps null geodesics. This surface is called the photon sphere.
We will show that the Schwarzschild spacetimes of positive mass are the only static vacuum asymptotically flat general relativistic spacetimes that possess a suitably geometrically defined photon sphere. We will present two proofs, both extending classical static black hole uniqueness results. Part of this work is joint with Gregory J. Galloway. As a corollary, we obtain a new result concerning the static n-body problem.<a href="http://www.math.uni-tuebingen.de/arbeitsbereiche/gadr/personen/dr-carla-cederbaum-1/dr-carla-cederbaum">Carla Cederbaum</a> (Universitat Tubingen)2016-03-28T12:00:00-04:009500geometry/topologyGeometry/topology SeminarMon, 28 Mar 2016 12:00:00 EDT205 PhysicsSpring, 2016Mon, 28 Mar 2016 13:00:00 EDTMonday, March 28, 2016, 12:00pmOn the Inviscid Limit of the Navier-Stokes Equations with Dirichlet Boundary Conditions
https://services.math.duke.edu/mcal?abstract-9388
We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the Navier-Stokes solutions remain bounded in $L^2_t L^\infty_x$ independently of the kinematic viscosity, and if they are equicontinuous at $x_2 = 0$. These conditions imply that there is no boundary layer separation: the Lagrangian paths originating in a boundary layer, stay in a proportional boundary layer during the time interval considered. We then give a proof of the (numerical) conjecture of vanDommelen and Shen (1980) which predicts the finite time blowup of the displacement thickness in the Prandtl boundary layer equations. This shows that the Prandtl layer exhibits separation in finite time.Vlad Vicol (Princeton University)2016-03-28T16:30:00-04:009388applied math and analysisApplied Math And Analysis SeminarMon, 28 Mar 2016 17:30:00 EDTSpring, 2016Monday, March 28, 2016, 4:30pmMon, 28 Mar 2016 16:30:00 EDT119 PhysicsMulti-scale simulation of crystal defects
https://services.math.duke.edu/mcal?abstract-9564
PART 1: I will construct a mathematical model of a defect embedded in an infinite homogeneous crystal. I will then establish a regularity result for minimisers, which given the crucial information on which approximation schemes are based. As an elementary application of this framework I will prove convergence rates for two computational schemes: (1) clamped far-field and (2) coupling to harmonic far-field model. <br/>
PART 2: The conditions under which the theory of Part 1 holds are separability and locality of the total energy. In Part 2 I will show how for a tight-binding model (a minimalistic electronic structure model) these two condition arise. This analysis raises some interesting (open) questions.<br/>
PART 3: Finally, I will use the theory developed in PART 1 and PART 2 to construct and analyse a new family of QM/MM embedding schemes with rigorous error estimates.<a href="http://homepages.warwick.ac.uk/staff/C.Ortner/">Christoph Ortner</a> (University of Warwick)2016-03-29T10:00:00-04:009564applied math and analysisApplied Math And Analysis SeminarTue, 29 Mar 2016 11:00:00 EDTSpring, 2016Tuesday, March 29, 2016, 10:00amTue, 29 Mar 2016 10:00:00 EDT119 PhysicsGelation and densification of cement hydrates: a soft matter in construction
https://services.math.duke.edu/mcal?abstract-9416
5-8 % of the global human CO2 production comes from the production of
cement, concrete main binder. The material strength emerges through the
development, once in contact with water, of calcium-silicate-hydrate (C-S-H)
gels that literally glue together the final compound. Current industrial
research aims at exploring alternative and more environmentally friendly
chemical compositions while enhancing rheology and mechanics, to overcome
the many technological challenges and guarantee concrete standards.
Identifying the fundamental mechanisms that control the gel properties at
the early stages of hydration and setting is crucial, although challenging,
because of far-from-equilibrium conditions, closely intertwined to the
evolution of the chemical environment, that are a hallmark of cement
hydration.
<br>
I will discuss a recently developed statistical physics approach, which
allows us to investigate the gel formation under the out-of-equilibrium
conditions typical of cement hydration and the role of the nano-scale
structure in C-S-H mechanics upon hardening. Our approach, combining Monte
Carlo and Molecular Dynamics simulations, unveils for the first time how
some distinctive features of the kinetics of cement hydration can be related
to the nano-scale effective interactions and to the changes in the
morphology of the gels. The novel emerging picture is that the changes of
the physico-chemical environment, which dictate the evolution of the
effective interactions, specifically favor the gel formation and its
continuous densification. Our findings provide new handles to design
properties of this complex material and an extensive comparison of numerical
findings for the hardened paste with experiments ranging from SANS, SEM,
adsorption/desorption of N2 and water to nano-indentation provide new,
fundamental insights into the microscopic origin of the properties measured.
<br>
K. Ioannidou, R.J.-M. Pellenq and E. Del Gado Controlling local packing and
growth in calcium-silicate-hydrate gels
<http://pubs.rsc.org/en/content/articlelanding/2013/sm/c3sm52232f#%21divAbstract>, Soft Matter 10, 1121 (2014)
<br>
E. Del Gado, K. Ioannidou, E. Masoero, A. Baronnet, R. J.-M. Pellenq, F. J.
Ulm and S. Yip, A soft matter in construction - Statistical physics approachfor formation and mechanics of C--S--H gels in cement,
<http://epjst.epj.org/articles/epjst/abs/2014/11/epjst22311015/epjst22311015.html>Eur. Phys. J. - ST 223, 2285 (2014).
<br>
K. Ioannidou, K.J. Krakowiak, M. Bauchy, C.G. Hoover, E. Masoero, S. Yip,
F.-J. Ulm, P. Levitz, R.J.-M. Pellenq and E. Del Gado, The mesoscale textureof cement hydrates
<http://www.pnas.org/content/early/2016/02/04/1520487113>, PNAS 113, 2029
(2016)**
<br>
K. Ioannidou, M. Kanduc, L. Li, D. Frenkel, J. Dobnikar and E. Del Gado,
The crucial effect of early-stage gelation on the mechanical properties of
cement hydrates , under review<a href="https://physics.georgetown.edu/users/emanuela-delgado">Emanuela Del Gado</a> (Dept of Physics, Georgetown)2016-03-29T15:00:00-04:009416CNCSCNCS SeminarTue, 29 Mar 2016 15:00:00 EDT119 PhysicsSpring, 2016Tue, 29 Mar 2016 16:00:00 EDTTuesday, March 29, 2016, 3:00pmMulti-scale simulation of crystal defects
https://services.math.duke.edu/mcal?abstract-9565
PART 1: I will construct a mathematical model of a defect embedded in an infinite homogeneous crystal. I will then establish a regularity result for minimisers, which given the crucial information on which approximation schemes are based. As an elementary application of this framework I will prove convergence rates for two computational schemes: (1) clamped far-field and (2) coupling to harmonic far-field model. <br/>
PART 2: The conditions under which the theory of Part 1 holds are separability and locality of the total energy. In Part 2 I will show how for a tight-binding model (a minimalistic electronic structure model) these two condition arise. This analysis raises some interesting (open) questions.<br/>
PART 3: Finally, I will use the theory developed in PART 1 and PART 2 to construct and analyse a new family of QM/MM embedding schemes with rigorous error estimates.<a href="http://homepages.warwick.ac.uk/staff/C.Ortner/">Christoph Ortner</a> (University of Warwick)2016-03-31T10:00:00-04:009565applied math and analysisApplied Math And Analysis SeminarThu, 31 Mar 2016 10:00:00 EDT119 PhysicsThu, 31 Mar 2016 11:00:00 EDTSpring, 2016Thursday, March 31, 2016, 10:00amHistory, Subversive Geographies and Neighborhood Data
https://services.math.duke.edu/mcal?abstract-9532
In modern urban research raw data, whether it represents people or our built environment, is generally summarized to boundaries created by our programs (think Census Bureau, city planning, place-based initiatives). But they keep changing, making it very hard to describe things we care a lot about through history. Housing conditions, household income, access to jobs and services data for these can seem less and less powerful because of the influence of changing boundaries over time. But they are also influenced by the presence of competing, often unacknowledged boundaries, both new and old. Methods exist for synthesizing Census geography from decade to decade. But how do we acknowledge the influence of these alternative geographies which have the power to influence home values and neighborhood stability, and can attract or discourage investment?John Killeen (Durham Neighborhood Compass)2016-03-31T11:45:00-04:009532Data DialogueData DialogueThu, 31 Mar 2016 11:45:00 EDTGross 330Spring, 2016Thu, 31 Mar 2016 12:45:00 EDTThursday, March 31, 2016, 11:45amScalar conservation laws with Markov initial data
https://services.math.duke.edu/mcal?abstract-9325
The inviscid Burgers' equation has the remarkable property
that its dynamics preserve the class of spectrally negative L\'{e}vy
initial data, as observed by Carraro and Duchon (statistical
solutions) and Bertoin (entropy solutions). Further, the evolution of
the L\'{e}vy measure admits a mean-field description, given by the
Smoluchowski coagulation equation with additive kernel. In this talk
we discuss ongoing efforts to generalize this result to scalar
conservation laws, a special case where this is done, and a connection
with integrable systems. Includes work with F. Rezakhanlou.<a href="http://www.dam.brown.edu/people/dkaspar/">David Kaspar</a> (Brown University)2016-03-31T16:30:00-04:009325probabilityProbability SeminarThursday, March 31, 2016, 4:30pmThu, 31 Mar 2016 17:30:00 EDTSpring, 2016119 PhysicsThu, 31 Mar 2016 16:30:00 EDTArtificially-induced synaptic plasticity in motor cortex: a theoretical model of a bidirectional brain-computer interface
https://services.math.duke.edu/mcal?abstract-9477
Experiments on macaque monkeys show that spike-triggered stimulation performed by a Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen synaptic connections between distant neural sites in Motor Cortex (MC) and even between MC and spinal cord, with changes that last several days. Here, a neural implant records from some neurons in MC and electrically stimulates others after set delays. The working hypothesis is that this stimulation procedure, which interacts with the very fast spiking activity of cortical circuits (on the order of milliseconds), induces changes mediated by synaptic plasticity mechanisms on much longer timescales (hours and days). The field of online, closed-loop BBCI's is rapidly evolving, with applications ranging from a science-oriented tool to clinical treatments of motor injuries. However, with the enhanced capability of novel devices that can record and stimulate an ever-growing number of neural sites comes growing complexity. It is therefore crucial to develop a theoretical understanding of the effects of closed-loop artificial stimulation in the highly recurrent neural circuits found in cortex, and how such protocols affect functional cotex-to-muscle mappings across a range of timescales.
In parallel with ongoing experiments, we are developing a mathematical model of recurrent MC networks with probabilistic spiking mechanisms and spike-time-dependent plastic synapses (STDP) capable of capturing both neural and synaptic activity statistics relevant to BBCI protocols. This model successfully reproduces key experimental results and we use analytical derivations to predict optimal operational regimes for BBCIs. We make experimental predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity such as awake behaving states or sleep. Importantly, this work provides a first step toward a theoretical framework aimed at the design and development of next-generations applications of BBCI's.<a href="http://faculty.washington.edu/glajoie/wordpress/?page_id=33">Guillaume Lajoie</a> (U. Washington Inst for Neuroengineering)2016-04-01T12:00:00-04:009477mathematical biologyMathematical Biology Seminar119 PhysicsFri, 01 Apr 2016 12:00:00 EDTFriday, April 1, 2016, 12:00pmFri, 01 Apr 2016 13:00:00 EDTSpring, 2016A Look at Branching Processes
https://services.math.duke.edu/mcal?abstract-9443
In 1873, a man named Francis Galton posed a question in Educational Times, calling for the mathematical study of the extinction of family surnames over time. Within a year, mathematician Henry Watson replied with a solution. But instead of ending there, this question opened up a new direction of mathematics: the study of branching processes. A branching process is a particle system in which the particles undergo splitting or branching events dictated by particular rules. This talk will introduce some examples of these systems (from the basic Galton-Watson model to more general branching-selection models), interesting questions people ask about branching processes, and some recent research done in this area.<a href="https://fds.duke.edu/db/aas/math/grad/ebeckman">Erin Beckman</a> (Duke University)2016-04-04T12:00:00-04:009443Graduate-FacultyGraduate/faculty SeminarMon, 04 Apr 2016 12:00:00 EDT119 PhysicsMon, 04 Apr 2016 13:00:00 EDTSpring, 2016Monday, April 4, 2016, 12:00pmApproximations to boundary value problems for nonlinear collisional kinetic plasma models
https://services.math.duke.edu/mcal?abstract-9506
We will discuss recent approximations to boundary value problems to non-linear systems of Boltzmann or Landau (for Coulombic interactions) equations coupled to the Poisson equation. The proposed approximation methods involve hybrid schemes of spectral and Galerkin type, were conservation of flow invariants are achieved by a constrain minimization problem. We will discuss some analytical and computational issues related to these approximations.Irene Gamba (University of Texas at Austin)2016-04-04T16:30:00-04:009506applied math and analysisApplied Math And Analysis SeminarMon, 04 Apr 2016 17:30:00 EDTSpring, 2016Monday, April 4, 2016, 4:30pmMon, 04 Apr 2016 16:30:00 EDT119 PhysicsExploiting disorder for global response: independence of bond-level contributions
https://services.math.duke.edu/mcal?abstract-9574
We are customarily taught to understand ordinary solids by considering perturbations about a perfect crystal. This approach becomes increasingly untenable as the amount of disorder in the solid increases; for a glass with no well-defined long-range order, a crystal is a terrible starting point for understanding the glasss rigidity or its excitations. Is there an alternative the opposite of a crystal where order, rather than disorder is the perturbation? Jamming is an alternate way of creating rigid solids that are qualitatively different from crystals.
In a crystal with only one atom per unit cell, all atoms play the same role in producing the solid's global response to external perturbations. Jammed disordered materials are not similarly constrained and a new principle emerges: independence of bond-level response. Using networks where individual bonds can be successively removed, one can drive the overall system to different regimes of behavior. Consequently one can exploit disorder to achieve unique, varied, textured and tunable global response.<a href="http://nagelgroup.uchicago.edu/Nagel-Group/index.html">Sidney Nagel</a> (The University of Chicago)2016-04-05T15:00:00-04:009574CNCSCNCS SeminarTue, 05 Apr 2016 15:00:00 EDT119 PhysicsTue, 05 Apr 2016 16:00:00 EDTSpring, 2016Tuesday, April 5, 2016, 3:00pmDegenerate ellipticity and the porous media equation
https://services.math.duke.edu/mcal?abstract-9502
In the first lecture I will give a brief discussion of local and non local diffusion and degenerate ellipticity and different local and non local models for compressible flows in porous media. <br/>
In the second and third lectures I will discuss some properties of the
(infinitesimal) porous media equation, a non local in space model and
equations with memory.<a href="http://www.ma.utexas.edu/users/caffarel/">Luis Caffarelli</a> (University of Texas at Austin)2016-04-05T16:30:00-04:009502Gergen LecturesGergen Lectures SeminarSpring, 2016Tue, 05 Apr 2016 17:30:00 EDTTuesday, April 5, 2016, 4:30pmTue, 05 Apr 2016 16:30:00 EDTPhysics 128Modular symbols and arithmetic
https://services.math.duke.edu/mcal?abstract-9462
I will explain how to attach ideal classes of cyclotomic
fields to geodesics in the complex upper half-plane. A conjecture of
mine states this construction is inverse to another arising from the
Galois action on cohomology of modular curves modulo an Eisenstein
ideal. I hope to use this to motivate a broader philosophy, developed
jointly with Takako Fukaya and Kazuya Kato, that certain arithmetic
objects attached to Galois representations of global fields can be
described using higher-dimensional modular symbols.<a href="http://math.arizona.edu/~sharifi/">Romyar Sharifi</a> (University of Arizona)2016-04-06T13:30:00-04:009462Number TheoryNumber Theory SeminarWed, 06 Apr 2016 13:30:00 EDT119 PhysicsWed, 06 Apr 2016 14:30:00 EDTSpring, 2016Wednesday, April 6, 2016, 1:30pmPositive Legendrian isotopies and Floer theory
https://services.math.duke.edu/mcal?abstract-9454
In a cooriented contact manifold, a positive Legendrian
isotopy is a Legendrian isotopy evolving in the positive transverse
direction to the contact plane. Their global behavior differs from the
one of Legendrian isotopy and is closer to the one of propagating waves.
After having introduce the basic definitions and main examples, I will
explain how to use information in the Floer complex associated to a pair
of Lagrangian cobordisms (recently constructed in a collaboration with
G. Dimitroglou Rizell, P. Ghiggini and R. Golovko) to give obstructions
to certain positive loops of some Legendrian submanifolds. This will
recover previously known obstructions and exhibit more examples. This is
work in progress with V. Colin and G. Dimitroglou Rizell.<a href="http://www.math.sciences.univ-nantes.fr/~chantraine-b/">Baptiste Chantraine</a> (Université de Nantes)2016-04-06T15:00:00-04:009454geometry/topologyGeometry/topology SeminarWednesday, April 6, 2016, 3:00pmWed, 06 Apr 2016 16:00:00 EDTSpring, 2016299 PhysicsWed, 06 Apr 2016 15:00:00 EDTDegenerate ellipticity and the porous media equation
https://services.math.duke.edu/mcal?abstract-9503
In the first lecture I will give a brief discussion of local and non local diffusion and degenerate ellipticity and different local and non local models for compressible flows in porous media. <br/>
In the second and third lectures I will discuss some properties of the
(infinitesimal) porous media equation, a non local in space model and
equations with memory.<a href="http://www.ma.utexas.edu/users/caffarel/">Luis Caffarelli</a> (University of Texas at Austin)2016-04-06T16:30:00-04:009503Gergen LecturesGergen Lectures SeminarWednesday, April 6, 2016, 4:30pmSpring, 2016Wed, 06 Apr 2016 17:30:00 EDTPhysics 119Wed, 06 Apr 2016 16:30:00 EDTFrom EHR to insight: Using electronic health records to generate novel, non-intuitive hypotheses for translational research
https://services.math.duke.edu/mcal?abstract-9536
Careful and perceptive clinical observations have frequently underpinned groundbreaking biomedical research. Many important research questions and subsequent discoveries have arisen from clinicians paying close attention to their patients. However, this approach is inherantly limited by the information-gathering and perceptual abilities of the human mind. The emergence of electronic health records (EHRs) and the concurrent advancement of statistical learning techniques now offers the opportunity scale up and enhance the "bedisde-to-bench" approach of the past. In this seminar, we will explore how application of data mining and statistical learning techniques to EHR data could be leveraged to generate novel hypotheses about disease mechanisms and associations, the insights from which could then be used to drive new experimental studies in the laboratory. We will discuss the potential application of this health data-driven approach in the context of chronic pain following major surgeries, such as thoractomy and amputation.Alexander Chamessian 2016-04-07T11:45:00-04:009536Data DialogueData DialogueGross 330Thu, 07 Apr 2016 11:45:00 EDTThursday, April 7, 2016, 11:45amSpring, 2016Thu, 07 Apr 2016 12:45:00 EDTAlgebraicity of automorphic representations
https://services.math.duke.edu/mcal?abstract-9542
One striking implication of Langlands' conjectures for
number fields is that many automorphic representations which are
initially defined by analytic and/or representation-theoretic means
should have deep algebro-geometric properties, ranging from the
algebraicity of Hecke eigenvalues, to the existence of associated
Galois representations and ultimately pure motives. An example of a
long-standing open problem in this area which admits an elementary
formulation is to prove that Maass forms of eigenvalue 1/4 have
algebraic Hecke eigenvalues. Two approaches have been used to verify
Langlands' predictions: (1) Finding and exploiting a direct link with
algebraic geometry and (2) Using Langlands' Functoriality Principle. I
will discuss the possibilities and limitations of the two approaches
and report on recent work on each approach. The results using the
geometric approach are joint work with Jean-Stefan Koskivirta, see
arXiv:1507.05032.<a href="https://wumath.wustl.edu/people/wushi-goldring">Wushi Goldring</a> (Washington U in St. Louis)2016-04-07T13:05:00-04:009542geometry/topologyGeometry and Number Theory Seminar130 PhysicsThu, 07 Apr 2016 13:05:00 EDTThursday, April 7, 2016, 1:05pmThu, 07 Apr 2016 14:05:00 EDTSpring, 2016Degenerate ellipticity and the porous media equation
https://services.math.duke.edu/mcal?abstract-9504
In the first lecture I will give a brief discussion of local and non local diffusion and degenerate ellipticity and different local and non local models for compressible flows in porous media. <br/>
In the second and third lectures I will discuss some properties of the
(infinitesimal) porous media equation, a non local in space model and
equations with memory.<a href="http://www.ma.utexas.edu/users/caffarel/">Luis Caffarelli</a> (University of Texas at Austin)2016-04-07T16:30:00-04:009504Gergen LecturesGergen Lectures SeminarThu, 07 Apr 2016 17:30:00 EDTSpring, 2016Thursday, April 7, 2016, 4:30pmThu, 07 Apr 2016 16:30:00 EDTPhysics 119Applications of stochastic models of carcinogenesis in cancer prevention
https://services.math.duke.edu/mcal?abstract-9479
Carcinogenesis is the transformation of normal cells into cancer cells. This process has been shown to be of a multistage nature, with stem cells that go through a series of (stochastic) genetic and epigenetic changes that eventually lead to a malignancy. Since the origins of the multistage theory in the 1950s, mathematical modeling has played a prominent role in the investigation of the mechanisms of carcinogenesis. In particular, two stochastic (mechanistic) models, the Armitage-Doll and the two-stage clonal expansion (TSCE) model, have been widely used in the past for cancer risk assessment and for the analysis of cancer population and experimental data. In this talk, I will introduce some of the biological and mathematical concepts behind the theory of multistage carcinogenesis, and discuss in detail the use of these models in cancer epidemiology and cancer prevention and control. Recent applications of multistage and state-transition Markov models to assess the potential impact of lung cancer screening in the US will be reviewed.<a href="https://sph.umich.edu/faculty-profiles/meza-rafael.html">Rafael Meza</a> (Michigan)2016-04-08T12:00:00-04:009479mathematical biologyMathematical Biology SeminarSpring, 2016Fri, 08 Apr 2016 13:00:00 EDTFriday, April 8, 2016, 12:00pmFri, 08 Apr 2016 12:00:00 EDT119 PhysicsMixed boundary conditions for a simplified quantum energy-transport model in multi-dimensional domains
https://services.math.duke.edu/mcal?abstract-9582
In this talk we consider the existence of suitable weak solutions for a quantum energy-transport model for semiconductors. The model is formally derived from the quantum hydrodynamic model by J\"{u}ngel and Mili\v{s}i\'{c} (Nonlinear Anal.: Real World Appl., 12(2011), pp. 1033-1046). It consists of a fourth-order nonlinear parabolic equation
for the electron density, an elliptic equation for the electron temperature, and the Poisson equation for the electric potential. Our solution is global in the time variable, while the space variables lie in a bounded Lipschitz domain with a mixed boundary condition. The existence proof is based upon a carefully-constructed approximation scheme which generates a sequence of positive approximate solutions. These solutions are shown to be so regular that they can be used to form a variety of test functions , from which we can derive enough a prior estimates to justify passing to the limit in the approximate problems.Xiangsheng Xu (Mississippi State University)2016-04-08T15:00:00-04:009582Department of MathematicsSpecial Talk Applied Math And Analysis SeminarFri, 08 Apr 2016 15:00:00 EDTPhysics 119Fri, 08 Apr 2016 16:00:00 EDTSpring, 2016Friday, April 8, 2016, 3:00pmSurface hopping: Mystery and opportunities for mathematicians
https://services.math.duke.edu/mcal?abstract-9431
Surface hopping is a very popular approach in theoretical chemistry for
mixed quantum-classical dynamics.
Yes, the above sentence looks scary. Let us start over again ...
We will examine from a mathematical point of view how stochastic
trajectories can be used to approximate solutions to a Schrodinger
equation (which is different from what Feynman did). Besides some
applications in chemistry, this is a nice topic since it combines ideas
from asymptotic analysis, applied probability, and applied harmonic
analysis.
The only background assumed in this talk is "separation of variables"
(and of course some PDEs where separation of variables is applied to).<a href="http://www.math.duke.edu/~jianfeng/">Jianfeng Lu</a> (Duke University)2016-04-11T12:00:00-04:009431Graduate-FacultyGraduate/faculty SeminarMon, 11 Apr 2016 13:00:00 EDTSpring, 2016Monday, April 11, 2016, 12:00pmMon, 11 Apr 2016 12:00:00 EDT119 PhysicsOn long-time behavior of 2d flows
https://services.math.duke.edu/mcal?abstract-9447
Our knowledge of the long-time behavior of 2d inviscid flows
is quite limited. There are some appealing conjectures based on ideas
in Statistical Mechanics, but they appear to be beyond reach of the
current methods. We will discuss some partial results concerning the
dynamics, as well as some results for variational problems to which
the Statistical Mechanics methods lead.Vladimir Sverak (University of Minnesota)2016-04-11T16:30:00-04:009447applied math and analysisApplied Math And Analysis Seminar119 PhysicsMon, 11 Apr 2016 16:30:00 EDTMonday, April 11, 2016, 4:30pmMon, 11 Apr 2016 17:30:00 EDTSpring, 2016Statistics of connectivity in networks optimizing information storage
https://services.math.duke.edu/mcal?abstract-9578
Brains have an impressive ability to store information about the
external world on time scales that range from seconds to years.
The rules of information storage in neuronal circuits are the
subject of ongoing debate. Two scenarios have been proposed by
theorists: In the first scenario, specific patterns of activity
representing external stimuli become fixed point attractors of the
dynamics of the network. In the second, the network stores
sequences of patterns of network activity so that when the first
pattern is presented the network retrieves the whole sequence. In
both scenarios, the correct dynamics are achieved thanks to
appropriate changes in network connectivity. I will describe how
methods from statistical physics can be used to investigate the
storage capacity of such networks, and the statistical properties
of network connectivity that optimizes information storage
(distribution of synaptic weights, probabilities of specific
network motifs, degree distributions, etc) in both scenarios.
Finally, I will compare the theoretical results with available data
on cortical connectivity.<a href="https://galton.uchicago.edu/~nbrunel/">Nicolas Brunel</a> (University of Chicago)2016-04-12T15:00:00-04:009578CNCSCNCS SeminarTue, 12 Apr 2016 16:00:00 EDTSpring, 2016Tuesday, April 12, 2016, 3:00pmTue, 12 Apr 2016 15:00:00 EDT119 PhysicsSingularities of area minimizing surfaces
https://services.math.duke.edu/mcal?abstract-9576
In a very large monograph of the late 70s Almgren provided a deep analysis of the singular set of area minimizing surfaces in codimension higher than 1. I will explain how a more modern approach reduces the proof to a manageable size and allows to go beyond his groundbreaking theorem.<a href="http://user.math.uzh.ch/delellis/">Camillo De Lellis</a> (Universitat Zurich)2016-04-13T15:15:00-04:009576geometry/topologyGeometry/topology SeminarWed, 13 Apr 2016 16:15:00 EDTSpring, 2016Wednesday, April 13, 2016, 3:15pmWed, 13 Apr 2016 15:15:00 EDT259 PhysicsOn Chow groups of Varieties
https://services.math.duke.edu/mcal?abstract-9549
For a complex algebraic variety, the Chow group is a geometric invariant which is easy to construct but often difficult to compute. In this talk, I will describe the construction of the Chow group, give some key examples and discuss some difficult open questions. I will also present a result about the Chow group of 0-cycles of the surface which parametrizes lines on a cubic 3-fold.Humberto Diaz (Duke)2016-04-13T16:30:00-04:009549algebraic geometryAlgebraic Geometry SeminarWed, 13 Apr 2016 17:30:00 EDTSpring, 2016Wednesday, April 13, 2016, 4:30pmWed, 13 Apr 2016 16:30:00 EDT119 PhysicsHow cultural networks shape public deliberation about autism advocacy on social media sites
https://services.math.duke.edu/mcal?abstract-9538
Social media sites are rapidly becoming one of the most important forums for public deliberation about advocacy issues. Yet social scientists have not yet explained why some advocacy organizations produce social media messages that inspire far ranging conversation among social media users, while the vast majority of them receive little or no attention. I combine network analysis and natural language processing to identify how the clustering of substantive topics within public conversations about Autism Spectrum Disorders enables and constrains advocacy organizations as they attempt to shape public discourse about this issue. I created a Facebook application that offered these organizations a complimentary audit of their social media strategy in return for sharing public and non-public data about their organization, its audience, and the broader social context in which they interact. Using time series models, I identify ideal positions within discursive networks that stimulate public conversation. I thereby contribute a novel theory of cultural framing, new network-based techniques for automated text analysis, and describe the promise of social media applications for social science research.<a href="http://www.chrisbail.net/">Christopher Bail</a> 2016-04-14T11:45:00-04:009538Data DialogueData DialogueThu, 14 Apr 2016 12:45:00 EDTSpring, 2016Thursday, April 14, 2016, 11:45amThu, 14 Apr 2016 11:45:00 EDTGross 330Moderate Deviation Principles for Weakly Interacting Particle Systems
https://services.math.duke.edu/mcal?abstract-9589
Moderate deviation principles for empirical measure processes
associated with weakly interacting Markov processes are established.
Two families of models are considered: the first corresponds to a
system of interacting diffusions whereas the second describes a
collection of pure jump Markov processes with a countable state space.
For both cases the moderate deviation principle is formulated in terms
of a large deviation principle (LDP), with an appropriate speed
function, for suitably centered and normalized empirical measure
processes. For the first family of models the LDP is established in
the path space of an appropriate Schwartz distribution space whereas
for the second family the LDP is proved in the space of
(the Hilbert space of square summable sequences)-valued paths. Proofs
rely on certain variational representations for exponential
functionals of Brownian motions and Poisson random measures. This is
joint work with Amarjit Budhiraja.Ruoyu Wu (UNC-Chapel Hill)2016-04-14T16:30:00-04:009589probabilityProbability SeminarTBDThu, 14 Apr 2016 16:30:00 EDTThursday, April 14, 2016, 4:30pmThu, 14 Apr 2016 17:30:00 EDTSpring, 2016Modeling the role of the immune response in chronic myelogenous leukemia
https://services.math.duke.edu/mcal?abstract-9481
Tyrosine kinase inhibitors (TKIs), such as imatinib (IM), have significantly improved treatment of chronic myelogenous leukemia (CML). However, the majority of patients are not cured for undetermined reasons. It turns out that many patients who otherwise responded well to IM therapy still show variations in their BCR-ABL transcripts.
In this talk we will overview mathematical models for leukemia, drug resistance, and stem cells. Our main focus will be on our recent results concerning mathematical models that integrate CML and an autologous immune response. This is a joint work with G. Clapp, T. Lepoutre, and F. Nicolini.<a href="http://www.math.umd.edu/~dlevy/">Doron Levy</a> (Maryland)2016-04-15T12:00:00-04:009481mathematical biologyMathematical Biology SeminarFri, 15 Apr 2016 13:00:00 EDTSpring, 2016Friday, April 15, 2016, 12:00pmFri, 15 Apr 2016 12:00:00 EDT119 PhysicsA world from a sheet of paper
https://services.math.duke.edu/mcal?abstract-9658
Take a sheet of paper. By folding, stacking, crumpling, tearing, we will tour a rich diversity of phenomena, from geometry and magic tricks to elasticity and the traditional Japanese art of origami. Much of the lecture consists of actual table-top demos, which you can try with family and friends. So then, take a sheet of paper.Tadashi Tokeida (Stanford University)2016-04-15T16:30:00-04:009658Public LecturesPLUM LecturesFri, 15 Apr 2016 17:30:00 EDTSpring, 2016Friday, April 15, 2016, 4:30pmFri, 15 Apr 2016 16:30:00 EDTPhysics 128TBA
https://services.math.duke.edu/mcal?abstract-9490
<a href="http://www.math.duke.edu/~jonm/">Jonathan Mattingly</a> (Duke University)2016-04-18T12:00:00-04:009490Graduate-FacultyGraduate/faculty SeminarMon, 18 Apr 2016 12:00:00 EDT119 PhysicsMon, 18 Apr 2016 13:00:00 EDTSpring, 2016Monday, April 18, 2016, 12:00pmDirichlet Graph Partitions
https://services.math.duke.edu/mcal?abstract-9348
Ill discuss a geometric approach to graph partitioning where the optimality criterion is given by the sum of the first Laplace-Dirichlet eigenvalues of the partition components. This eigenvalue optimization problem can be solved by a rearrangement algorithm, which we show to converge in a finite number of iterations to a local minimum of a relaxed objective. This partitioning method compares well to state-of-the-art approaches on a variety of graphs constructed from manifold discretizations, synthetic data, the MNIST handwritten digit dataset, and images. I'll present a consistency result for geometric graphs, stating convergence of graph partitions to an appropriate continuum partition.Braxton Osting (University of Utah)2016-04-18T16:30:00-04:009348applied math and analysisApplied Math And Analysis SeminarMon, 18 Apr 2016 16:30:00 EDT119 PhysicsMon, 18 Apr 2016 17:30:00 EDTSpring, 2016Monday, April 18, 2016, 4:30pmOn the Surfactant-Driven Fracture of Particulate Rafts
https://services.math.duke.edu/mcal?abstract-9424
Over the past decade, much attention has focused on the behavior of
hydrophobic particles at interfaces. These systems are of interest to
scientists and engineers, for example, due to their potential for
stabilizing drops and emulsions via jamming. This seminar will focus on the
behavior of particulate 'rafts' that form when a monolayer of particles are
placed at an air- liquid interface. The particles interact with the
underlying fluid to form a quasi two-dimensional solid. Such particulate
rafts can support both tension and compression, and they buckle under
sufficiently large compressive loads. When a drop of surfactant is
introduced into the system, fracture networks develop in the rafts. The
fracture process exhibits features observed in other elastic systems, such
as crack kinking, crack branching, and crack arrest. Moreover, there is a
clear coupling between the praft fracture and the diffusion of the
surfactant on the surface and through the 'porous' liquid-particle
monolayer. As such, one can draw analogies between this system and others
where crack growth interacts with fluid flow or mass transport.
The seminar will present recent work in modeling the diffusion of surfactant
into particle raft systems and the resulting formation of fracture networks.
We will present both discrete models that track the motion of individual
particles, as well as a new continuum model for poro-chemo-elasticity.
Results that reproduce some of the quantitative and qualitative aspects of
recent experimental studies of these systems will also be shown.<a href="http://cee.duke.edu/faculty/john-everett-dolbow">John Dolbow</a> (Dept of Civil Engineering, Duke University)2016-04-19T15:00:00-04:009424CNCSCNCS SeminarTue, 19 Apr 2016 16:00:00 EDTSpring, 2016Tuesday, April 19, 2016, 3:00pmTue, 19 Apr 2016 15:00:00 EDT119 PhysicsHOMFLY-PT homology of general link diagrams and its decategorification
https://services.math.duke.edu/mcal?abstract-9587
In the construction of HOMFLY-PT homology, one must start with a link presented as a braid closure. This restriction was expected by Khovanov and Rozansky to be required for the homology to be an isotopy invariant. In this talk, after reviewing the construction of the HOMFLY-PT polynomial and homology, we explore the consequences of dropping this requirement and allowing general link diagrams. We explicitly show that the Reidemeister IIb move (where the strands have opposite orientations) fails. Finally we will show that the Euler characteristic of this homology theory is a deformed version of the HOMFLY-PT polynomial which detects "braidlike" isotopy of tangles and links. This new polynomial agrees with the HOMFLY-PT polynomial on link diagrams which are presented as closed braid diagrams.<a href="https://services.math.duke.edu/~maabel/">Michael Abel</a> (Duke University)2016-04-19T16:30:00-04:009587geometry/topologyGeometry/topology SeminarTuesday, April 19, 2016, 4:30pmSpring, 2016Tue, 19 Apr 2016 17:30:00 EDT119 PhysicsTue, 19 Apr 2016 16:30:00 EDTReal structures on abelian varieties
https://services.math.duke.edu/mcal?abstract-9441
In this talk we describe a partially successful attempt to describe a characteristic p > 0 analog of the locally symmetric spaces for GL(n,R), by interpreting this as a "moduli space" for abelian varieties with real structure.Mark Goresky 2016-04-20T13:30:00-04:009441Number TheoryNumber Theory SeminarWed, 20 Apr 2016 13:30:00 EDT119 PhysicsSpring, 2016Wed, 20 Apr 2016 14:30:00 EDTWednesday, April 20, 2016, 1:30pmRational curves on hypersurfaces of low degree
https://services.math.duke.edu/mcal?abstract-9519
Tim Browning (University of Bristol)2016-04-20T16:30:00-04:009519Number TheoryNumber Theory SeminarWed, 20 Apr 2016 16:30:00 EDT119 PhysicsSpring, 2016Wed, 20 Apr 2016 17:30:00 EDTWednesday, April 20, 2016, 4:30pmEstimating the shape of climate and diet variation in the human skull: a mixed model approach
https://services.math.duke.edu/mcal?abstract-9540
In evolutionary studies, the beauty of shape analysis is its potential to both quantify and concretely represent biological variation. Ironically, preserving this potential while also accounting for evolutionary relationships has proven challenging. Here, I expand upon a recently developed mixed model for highly multivariate data in order to quantify shape change associated with climate and diet variation in a global sample of recent human crania and mandibles. The results provide subtle but clear evidence of the influence of climate and diet on human skull shape. The mixed model makes it possible, for the first time, to both account for evolutionary relationships and portray these changes in their native shape units.<a href="http://anthropology.ucdavis.edu/labs/paleoanthropology-1/people-1/david-katz/david-katz">David Katz</a> (UC Davis)2016-04-21T11:45:00-04:009540Data DialogueData DialogueSpring, 2016Thu, 21 Apr 2016 12:45:00 EDTThursday, April 21, 2016, 11:45amThu, 21 Apr 2016 11:45:00 EDTGross 330A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications
https://services.math.duke.edu/mcal?abstract-9656
During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.Mark Goresky (Institute for Advanced Study)2016-04-21T16:30:00-04:009656Public LecturesPLUMPhysics 128Thu, 21 Apr 2016 16:30:00 EDTThursday, April 21, 2016, 4:30pmThu, 21 Apr 2016 17:30:00 EDTSpring, 2016Probabilistic symmetries in networks
https://services.math.duke.edu/mcal?abstract-9327
I discuss various refinements and extensions of the principle of exchangeability, focusing on 3 specific cases:
1. Relative exchangeability, by which the distribution of a random graph is invariant with respect to the symmetries of some other structure.
2. Combinatorial Markov processes for temporally varying networks.
3. Edge exchangeable random graphs, a new invariance principle that resolves a major challenge in modeling network datasets that are sparse and/or exhibit power law degree distributions.
Each case leads to a characterization theorem that parallels prior work by Aldous-Hoover-Kallenberg (in case 1), Levy-Ito-Khintchine (in case 2), and de Finetti and Kingman (in case 3). Though the discussion applies more generally, I phrase much of the presentation in the specific context of random graphs.<a href="http://stat.rutgers.edu/home/hcrane/">Harry Crane</a> (Rutgers University)2016-04-21T16:30:00-04:009327probabilityProbability SeminarThursday, April 21, 2016, 4:30pmSpring, 2016Thu, 21 Apr 2016 17:30:00 EDTUNC, Gardner 210Thu, 21 Apr 2016 16:30:00 EDTTargeting the phenotype: Treatment strategies for heterogeneous cancer
https://services.math.duke.edu/mcal?abstract-9483
Targeted cancer drugs attack pathway specific phenotypes and can lead to very positive outcomes when a particular phenotype dominates the population of a specific tumor. However, these drugs often fail because not all cells express the targeted phenotype to the same degree. This leads to a heterogeneous response to treatment, and ultimate recurrence of the cancer as sensitive cells die off and resistant cells take over. We explore how treatment strategies informed by a tumors phenotypic mix, can help slow the emergence of resistance and stave off tumor recurrence. We use an off-lattice agent-based model that incorporates inheritance of two phenotypes proliferation rate and migration speed and is modulated by a space limiting selection force. We find how and when distinct distributions of phenotypes require different treatment strategies.<a href="http://jillgallaher.flavors.me/">Jill Galagher</a> (Moffitt Cancer Institute)2016-04-22T12:00:00-04:009483mathematical biologyMathematical Biology SeminarFri, 22 Apr 2016 12:00:00 EDT119 PhysicsSpring, 2016Fri, 22 Apr 2016 13:00:00 EDTFriday, April 22, 2016, 12:00pmSpectral geometry and topology; Euler characteristic and analytic torsion
https://services.math.duke.edu/mcal?abstract-9496
What do eigenvalues have to do with geometry and topology? The first part of the talk will provide a few answers to that very broad question, including a discussion of the Euler characteristic from a spectral theory perspective. The second part of the talk will be a brief introduction to my research in analytic torsion, a topological invariant defined in terms of eigenvalues. In particular I'll explain some similarities and differences between analytic torsion and Euler characteristic.<a href="https://sites.google.com/site/phillipandreae/home">Phillip Andreae</a> (Duke University)2016-04-25T12:00:00-04:009496Graduate-FacultyGraduate/faculty SeminarMon, 25 Apr 2016 12:00:00 EDT119 PhysicsSpring, 2016Mon, 25 Apr 2016 13:00:00 EDTMonday, April 25, 2016, 12:00pmMaximal operators and Hilbert transforms along variable curve
https://services.math.duke.edu/mcal?abstract-9391
I will present several results on the boundedness of maximal operators and Hilbert transforms along variable curves and surfaces, in dimension two or higher. Connections to the circular maximal operator, and the polynomial Carleson operator will also be discussed.<a href="http://pages.iu.edu/~shaoguo/">Shaoming Guo</a> (Indiana University, Bloomington)2016-04-25T16:30:00-04:009391applied math and analysisApplied Math And Analysis SeminarMon, 25 Apr 2016 17:30:00 EDTSpring, 2016Monday, April 25, 2016, 4:30pmMon, 25 Apr 2016 16:30:00 EDT119 PhysicsOn motivic realizations for variations of Hodge structure of Calabi-Yau type over Hermitian symmetric domains
https://services.math.duke.edu/mcal?abstract-9460
Based on the work of Gross and Sheng-Zuo, Friedman and Laza have classified variations of real Hodge structure of Calabi-Yau type over Hermitian symmetric domains. In particular, over every irreducible Hermitian symmetric domain there exists a canonical variation of real Hodge structure of Calabi-Yau type. In this talk, we wil review Friedman and Lazas classification. A natural question to ask is whether the canonical Hermitian variations of Hodge structure of Calabi-Yau type come from families of Calabi-Yau manifolds (geometric realization). In general, this is very difficult and is still open for small dimensional domains. We will discuss an intermediate question, namely does the canonical variations occur in algebraic geometry as sub-variations of Hodge structure of those coming from families of algebraic varieties (motivic realization). In particular, we will give motivic realizations for the canonical variations of Calabi-Yau type over irreducible tube domains of type A using abelian varieties of Weil type.<a href="http://www.math.tamu.edu/people/formalpg.php?user=zzhang">Zheng Zhang</a> (Texas A&M University)2016-04-26T16:30:00-04:009460geometry/topologyGeometry/topology Seminar119 PhysicsTue, 26 Apr 2016 16:30:00 EDTTuesday, April 26, 2016, 4:30pmTue, 26 Apr 2016 17:30:00 EDTSpring, 2016Textured Image Deconvolution and Decomposition
https://services.math.duke.edu/mcal?abstract-9571
Approximation theory is at the heart of image analysis, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past several decades. The goal of this study is to illustrate a difficult issue in texture analysis of images which has forensic applications (e.g. to fingerprinting, ballistic images and shoe prints). In particular, it is known that texture information is almost destroyed by a blur operator, such as results from a ballistic image captured by a low-cost microscope. The contribution of this work is twofold. First, we propose a mathematical model for textured image deconvolution and decomposition into several meaningful components. That deconvolution uses a fourth-order PDE approach based on the directional mean curvature. Second, we discover a link between functional analysis and sampling theory, as in harmonic analysis and filter banks. This is preliminary work for a challenging project in estimation of image quality. It requires extensive pre-processing steps and approximation theory.
Joint work with David BanksHoang Duy Thai 2016-04-28T11:45:00-04:009571Data DialogueData DialogueGross 330Thu, 28 Apr 2016 11:45:00 EDTThursday, April 28, 2016, 11:45amSpring, 2016Thu, 28 Apr 2016 12:45:00 EDTSpatiotemporal integration of synaptic inputs in neurons: computational modeling, analysis and experiments
https://services.math.duke.edu/mcal?abstract-9585
A neuron receives thousands of synaptic inputs from other neurons and
integrates them to process information. Many experimental results
demonstrate this integration could be highly nonlinear, yet few
theoretical analyses have been performed to obtain a precise
quantitative characterization. Based on asymptotic analysis of an
idealized cable model, we derive a bilinear spatiotemporal integration
rule for a pair of time-dependent synaptic inputs. Note that the above
rule is obtained from idealized models. However, we have confirmed this
rule both in simulations of a realistic pyramidal neuron model and in
electrophysiological experiments of rat hippocampal CA1 neurons. Our
results demonstrate that the integration of multiple synaptic inputs can
be decomposed into the sum of all possible pairwise integration with
each paired integration obeying a bilinear rule.<a href="http://ins.sjtu.edu.cn/people/zdz/">Douglas Zhou</a> (Shanghai Jiao Tong University, Institute of Natural Sciences & Math Department,)2016-04-28T16:30:00-04:009585applied math and analysisApplied Math And Analysis Seminar119 PhysicsThu, 28 Apr 2016 16:30:00 EDTThursday, April 28, 2016, 4:30pmSpring, 2016Thu, 28 Apr 2016 17:30:00 EDTDigital biology: protein-ligand interactions
https://services.math.duke.edu/mcal?abstract-9485
The digital nature of biology is crucial to its functioning as an
information system, as well in building hierarchical components in
a repeatable way. We explain how protein systems can function as
discrete components, despite the importance of non-specific forces
due to the hydrophobic effect. That is, we address the question of
why proteins bind to ligands predictably and not in a continuous
distribution of places, the way grease forms into blobs.
We will give a detailed description of how data mining in the PDB
can reveal how proteins interact. We highlight the role of the
hydrophobic effect, but we see that it works inversely to the
usual concept of hydrophobic interaction.
Our work suggests the need for a more accurate model of the
dielectric effect in the vicinity of a protein surface, and we
discuss some advances in this direction. Our research also
provides an understanding of how molecular recognition and
signaling can evolve. We give an example of the use of our ideas
in drug design.<a href="http://people.cs.uchicago.edu/~ridg/">L. Ridgway Scott</a> (Chicago)2016-04-29T12:00:00-04:009485mathematical biologyMathematical Biology SeminarFri, 29 Apr 2016 12:00:00 EDT119 PhysicsFri, 29 Apr 2016 13:00:00 EDTSpring, 2016Friday, April 29, 2016, 12:00pmVibration and the local structure of elliptic partial differential equations
https://services.math.duke.edu/mcal?abstract-9580
If you put sand on a metal plate and start inducing vibrations with
a violin bow, the sand jumps around and arranges itself in the most beautiful patterns - this used to be a circus trick in the late 18th century: Napoleon was a big fan and put a prize on giving the best mathematical explanation. Today we know that the sand moves to lines where a certain Laplacian eigenfunction vanishes but these remain mysterious. I will show pictures of sand and demonstrate a new approach: the key ingredient is to make the elliptic equation parabolic and then work with two different interpretations of the heat equation at the same time. If time allows, I will sketch another application of this philosophy to localization phenomena for Schroedinger operators.<a href="mailto:stefan.steinerberger@gmail.com">Stefan Steinerberger</a> (Yale University)2016-05-02T16:30:00-04:009580applied math and analysisApplied Math And Analysis SeminarMon, 02 May 2016 16:30:00 EDT119 PhysicsSpring, 2016Mon, 02 May 2016 17:30:00 EDTMonday, May 2, 2016, 4:30pmDepartment [DELETED]
https://services.math.duke.edu/mcal?abstract-12979
Dept. Faculty Meeting 2024-03-22T10:30:00-04:0012979Department of MathematicsR.BryantFri, 22 Mar 2024 11:30:00 EDTSpring, 2024Friday, March 22, 2024, 10:30amFri, 22 Mar 2024 10:30:00 EDTdeletedPhysics 119TBA [DELETED]
https://services.math.duke.edu/mcal?abstract-12849
<a href="https://www.ihes.fr/~urbanik/">David Urbanik</a> (IHES)2024-03-29T13:30:00-04:0012849algebraic geometryAlgebraic Geometry SeminarFri, 29 Mar 2024 14:30:00 EDTSpring, 2024Friday, March 29, 2024, 1:30pmdeletedFri, 29 Mar 2024 13:30:00 EDTZoom linkTBA [DELETED] --- CANCELED
https://services.math.duke.edu/mcal?abstract-12874
<a href="https://spencerleslie.com/">Spencer Leslie</a> (Boston College, Mathematics)2024-04-10T15:15:00-04:0012874Number TheoryNumber Theory SeminarSpring, 2024Wed, 10 Apr 2024 15:15:00 EDTIntWednesday, April 10, 2024, 3:15pmdeletedWed, 10 Apr 2024 15:15:00 EDTPhysics 119TBA [DELETED]
https://services.math.duke.edu/mcal?abstract-12956
<a href="https://sites.google.com/view/jpark776/home">Jaemin Park</a> (University of Basel)2024-04-23T15:15:00-04:0012956Department of Mathematicsapplied math and analysisDepartment of Mathematics SeminarTuesday, April 23, 2024, 3:15pmSpring, 2024Tue, 23 Apr 2024 16:15:00 EDTPhysics 119deletedTue, 23 Apr 2024 15:15:00 EDT [DELETED]
https://services.math.duke.edu/mcal?abstract-12872
Mary Pugh (University of Pennsylvania)2024-05-11T11:00:00-04:0012872Department of MathematicsGraduation "SAVE THE DATE"Spring, 2024Sat, 11 May 2024 14:00:00 EDTSaturday, May 11, 2024, 11:00amdeletedSat, 11 May 2024 11:00:00 EDTOnsite