Department of Mathematics, Fall_2019
https://services.math.duke.edu/mcal?listgroup-0
Department of Mathematics Upcoming Seminarsen-us2024-03-28T05:46:10-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyMath Departmental meeting
https://services.math.duke.edu/mcal?abstract-10979
Jonathan Mattingly 2019-08-27T15:15:00-04:0010979Other Meetings and EventsMeetingTuesday, August 27, 2019, 3:15pmTue, 27 Aug 2019 15:15:00 EDTTue, 27 Aug 2019 16:15:00 EDT130 PhysicsFall, 2019Algebraic and tropical moduli spaces
https://services.math.duke.edu/mcal?abstract-10978
The moduli space of genus g Riemann surfaces, denoted M_g,
has been studied for more than a century, yet much of its geometry is
still a mystery. For example, in the 1980s Harer and Zagier showed
that the Euler characteristic (up to sign) grows super-exponentially
with g---yet most of this cohomology is not explicitly known. I will
give an introduction to M_g, and discuss recent results with Soren
Galatius and Sam Payne finding exponentially growing cohomology in
degree 4g-6, disproving a conjecture of Kontsevich; and a proof, with
Carel Faber, Galatius, and Payne, of a formula for top-weight Euler
characteristic of M_{g,n} conjectured by Zagier.<a href="https://www.math.brown.edu/~mtchan/">Melody Chan</a> (Brown University, Mathematics)2019-08-28T15:15:00-04:0010978algebraic geometryAlgebraic Geometry SeminarWednesday, August 28, 2019, 3:15pmWed, 28 Aug 2019 15:15:00 EDTInt119 PhysicsWed, 28 Aug 2019 16:15:00 EDThttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10977.jpg" /></div>
Fall, 2019Stability properties for functional and geometric inequalities and their applications
https://services.math.duke.edu/mcal?abstract-10976
Balls have the least perimeter of all sets of a fixed volume, and furthermore, any set with nearly optimal perimeter is close, in a suitably measured sense, to a ball. This latter statement reflects a stability property for the isoperimetric inequality. We will take a broad look at stability properties in various contexts, along with their applications to geometric problems. The talk includes joint work with several collaborators and will be accessible to a broad research audience.<a href="https://www.ias.edu/scholars/robin-neumayer">Robin Neumayer</a> (IAS)2019-08-30T12:00:00-04:0010976algebraic geometryapplied math and analysisApplied Math and AnalysisYesFri, 30 Aug 2019 12:00:00 EDTFriday, August 30, 2019, 12:00pmhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10975.jpg" /></div>
Fall, 2019Fri, 30 Aug 2019 13:00:00 EDT119 PhysicsCompactifications of moduli of points and lines in P<sup>2</sup>
https://services.math.duke.edu/mcal?abstract-10875
Projective duality identifies the moduli space B<sub>n</sub>
parametrizing configurations of n general points in projective 2-space P<sup>2</sup> with X(3,n), parametrizing configurations of n general lines in
the dual P<sup>2</sup>. When considering degenerations of such
objects, it is interesting to compare different compactifications of the
above moduli spaces. In this work, we consider Gerritzen-Piwek's
compactification of B<sub>n</sub> and Kapranov's Chow quotient
compactification of X(3,n), and we show they have
isomorphic normalizations. We also construct an alternative compactification which parametrizes all possible n-pointed central fibers of Mustafin joins associated to
one-parameter degenerations of n points in P<sup>2</sup>. This corrects
some of the results in Gerritzen-Piwek's paper. Finally, we describe
this alternative compactification for n=5,6. This is joint work in
progress with Jenia Tevelev.<a href="http://people.math.umass.edu/~schaffler/">Luca Schaffler</a> (U Mass)2019-08-30T15:15:00-04:0010875algebraic geometryAlgebraic GeometryFriday, August 30, 2019, 3:15pmFri, 30 Aug 2019 15:15:00 EDTFall, 2019Fri, 30 Aug 2019 16:15:00 EDT119 PhysicsThom polynomial and its K-theoretic generalization
https://services.math.duke.edu/mcal?abstract-10932
Global singularity theory originates from problems in obstruction theory. Consider the following question: is there an immersion in a given homotopy class of maps between two smooth compact manifolds M and N? We can reformulate this question as "is the set of points, where a generic smooth map between M and N is not an immersion, empty"? This set is the simplest example of a singularity. Alternatively, we can ask a question whether the cohomology class of this set is 0 or not. Turns out, there is a universal polynomial depending only on the dimensions of M and N and on the type of singularity, that, when evaluated in the corresponding characteristic classes of M and N, computes the cohomology class of a singularity. This polynomial is called the Thom polynomial, and it is the central notion of singularity theory.
In my talk I will give an introduction to singularity theory, define the classic Thom polynomial and talk about different approaches to its K-theoretic generalization.<a href="mailto:n.kolokolnikova@gmail.com">Natalia Kolokolnikova</a> (UNC)2019-09-02T15:15:00-04:0010932geometry/topologyGeometry SeminarYesMon, 02 Sep 2019 15:15:00 EDTMonday, September 2, 2019, 3:15pmFall, 2019119 PhysicsMon, 02 Sep 2019 16:15:00 EDTBridging MCMC and Optimization
https://services.math.duke.edu/mcal?abstract-10901
In this talk, I will discuss three ingredients of optimization theory in the context of MCMC: Non-convexity, Acceleration, and Stochasticity. <br/><br/>
I will focus on a class of non-convex objective functions arising from mixture models. For that class of objective functions, I will demonstrate that the computational complexity of a simple MCMC algorithm scales linearly with the model dimension, while optimization problems are NP-hard.<br/><br/>
I will then study MCMC algorithms as optimization over the KL-divergence in the space of measures. By incorporating a momentum variable, I will discuss an algorithm which performs "accelerated gradient descent" over the KL-divergence. Using optimization-like ideas, a suitable Lyapunov function is constructed to prove that an accelerated convergence rate is obtained.<br/><br/>
Finally, I will present a general recipe for constructing stochastic gradient MCMC algorithms that translates the task of finding a valid sampler into one of choosing two matrices. I will then describe how stochastic gradient MCMC algorithms can be applied to applications involving temporally dependent data, where the challenge arises from the need to break the dependencies when considering minibatches of observations.<a href="mailto:yianma@berkeley.edu">Yian Ma</a> (Google/UCSD)2019-09-04T12:00:00-04:0010901applied math and analysisApplied Math And Analysis SeminarWednesday, September 4, 2019, 12:00pmYesWed, 04 Sep 2019 12:00:00 EDTFall, 2019119 PhysicsWed, 04 Sep 2019 13:00:00 EDTGene Ferruzza, Valassis
https://services.math.duke.edu/mcal?abstract-10944
Data Dialogue with Gene Ferruzza, ValassisGene Ferruzza (Valassis)2019-09-06T11:45:00-04:0010944Data DialogueData DialogueFriday, September 6, 2019, 11:45amFri, 06 Sep 2019 11:45:00 EDTFall, 2019Gross Hall 103Fri, 06 Sep 2019 12:45:00 EDTSteenrod operations and the Artin-Tate pairing
https://services.math.duke.edu/mcal?abstract-10962
In 1966 Artin and Tate constructed a canonical pairing on the Brauer group of a surface over a finite field, and conjectured it to be alternating. This duality has analogous incarnations across arithmetic and topology, namely the Cassels-Tate pairing for a Jacobian variety, and the linking form on a 5-manifold. I will explain a proof of the conjecture, which is based on a surprising connection to Steenrod operations.<a href="mailto:fengt@mit.edu">Tony Feng</a> (MIT, Mathematics)2019-09-06T15:15:00-04:0010962Number TheoryNumber Theory SeminarFriday, September 6, 2019, 3:15pmYesFri, 06 Sep 2019 15:15:00 EDTFall, 2019119 PhysicsFri, 06 Sep 2019 16:15:00 EDTComplex monopoles
https://services.math.duke.edu/mcal?abstract-10907
The Bogomolny monopole equation can be complexified in many inequivalent ways, but there are two obvious options: One can extend Hodge duality in either a complex linear fashion, or in a conjugate linear one. The two cases result in two very different equations.
These equations are also the dimensional reductions of the 4-dimensional Haydys and Kapustin-Witten equations, respectively. Thus we call solutions of the first equations Haydys monopoles, while solutions of the second equations called Kapustin-Witten monopoles.
We find a stark contrast between the two cases: On one hand, we construct an open neighborhood of the Bogomolny moduli space within the Haydys moduli space, and show that this neighborhood is a smooth, hyperkahler manifold of dimension twice that of the Bogomolny moduli space.
On the other hand, we prove that a (finite energy) Kapustin-Witten monopole is necessarily a Bogomolny monopole when the structure group is SU(2).
(Joint work with Goncalo Oliveira)<a href="https://akosnagy.com">Akos Nagy</a> (Duke University, Mathematics)2019-09-09T15:15:00-04:0010907geometry/topologyGeometry/topology SeminarMonday, September 9, 2019, 3:15pmMon, 09 Sep 2019 15:15:00 EDTFall, 2019119 PhysicsMon, 09 Sep 2019 16:15:00 EDTThe contact process on random trees and graphs
https://services.math.duke.edu/mcal?abstract-10917
The contact process describes an elementary epidemic model, where each infected site gets healed at rate 1 while it passes its disease to each of its neighbors independently at rate \lambda. In this talk, we show that the phase diagram of the contact process on a Galton-Watson tree depends on the tail of the offspring distribution in the following sense: the extinction-survival threshold is strictly positive if and only if the tail has an exponential decay. In such cases, we further achieve the first-order asymptotics for the location of the threshold. We will also discuss analogous results for Erdos–Renyi and other random graphs.
Joint work with Shankar Bhamidi, Oanh Nguyen and Allan Sly.Danny Nam (Princeton)2019-09-12T15:15:00-04:0010917probabilityProbability SeminarFall, 2019Thu, 12 Sep 2019 16:15:00 EDT119 PhysicsThursday, September 12, 2019, 3:15pmThu, 12 Sep 2019 15:15:00 EDTMark Ritter, IBM
https://services.math.duke.edu/mcal?abstract-10919
TH Sept. 12
MLBytes Ahmadieh Grand Hall (GH 330)
Mark Ritter, IBMMark Ritter (IBM)2019-09-12T16:30:00-04:0010919Other Meetings and EventsMLBytes WorkshopThu, 12 Sep 2019 16:30:00 EDTThursday, September 12, 2019, 4:30pmThu, 12 Sep 2019 17:30:00 EDTGross Hall, Ahmadieh Family Grand Hall, Room 330Fall, 2019Jessilyn Dunn, Duke BME
https://services.math.duke.edu/mcal?abstract-10911
Data Dialogue
Jessilyn Dunn, Duke BME
11:45 - 1:00 p.m. (lunch provided, first come first serve)
Gross Hall 103Jessilyn Dunn (Duke BME)2019-09-13T11:45:00-04:0010911Data DialogueData DialogueFriday, September 13, 2019, 11:45amFri, 13 Sep 2019 11:45:00 EDTGross Hall 103Fri, 13 Sep 2019 13:00:00 EDTFall, 2019The Maximal Rank Conjecture
https://services.math.duke.edu/mcal?abstract-10985
Curves in projective space can be described by either parametric or
Cartesian equations. A natural question is how the parametric and
Cartesian descriptions of a curve relate to each other. We describe
the Maximal Rank Conjecture, formulated originally by Severi in 1915,
which prescribes a relationship between the "shape" of the parametric
and Cartesian equations --- i.e. which gives the Hilbert function of a
general curve of genus g, embedded in P^r via a general linear series
of degree d.
We then discuss the "interpolation problem" which asks how many
general points a curve of given type can pass through (for example a
line can pass through two general points but not three). We conclude
by sketching how recent results on the interpolation problem can be
used to prove the maximal rank conjecture.<a href="http://web.stanford.edu/~elarson3/">Eric Larson</a> (Stanford University, Mathematics)2019-09-13T15:15:00-04:0010985algebraic geometryAlgebraic Geometry SeminarFall, 2019https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/11010.jpg" /></div>
Physics 119Fri, 13 Sep 2019 16:15:00 EDTFriday, September 13, 2019, 3:15pmFri, 13 Sep 2019 15:15:00 EDTPeriodic paths on the pentagon
https://services.math.duke.edu/mcal?abstract-10888
Mathematicians have long understood periodic billiard trajectories on the square table, which occur when the slope of the trajectory is rational. In this talk, I'll explain my work on periodic trajectories on the regular pentagon, describing their geometry, symbolic dynamics, and group structure. The periodic trajectories are very beautiful, and some of them exhibit a surprising "dense but not equidistributed" behavior. There will be lots of pictures. This is joint work with Samuel Lelièvre.<a href="https://www.swarthmore.edu/NatSci/ddavis3/">Diana Davis</a> (Swarthmore College, Mathematics)2019-09-16T15:15:00-04:0010888geometry/topologyGeometry/topology SeminarMonday, September 16, 2019, 3:15pmYesMon, 16 Sep 2019 15:15:00 EDTFall, 2019119 PhysicsMon, 16 Sep 2019 16:15:00 EDTAsymptotic criticality of the Navier-Stokes regularity problem
https://services.math.duke.edu/mcal?abstract-10832
The purpose of this talk is to present a mathematical framework--based on a suitably defined 'scale of sparseness' of the super-level sets of the higher order spatial derivatives of the velocity field--in which the scaling gap between the regularity class and the corresponding a priori bound (in the vicinity of the possible singular time) shrinks to zero as the order of the derivative goes to infinity. This is a joint work with Liaosha Xu.Zoran Grujic (University of Virginia)2019-09-18T12:00:00-04:0010832applied math and analysisApplied Math And Analysis SeminarWed, 18 Sep 2019 12:00:00 EDTWednesday, September 18, 2019, 12:00pmPhysics 119Wed, 18 Sep 2019 13:00:00 EDTFall, 2019Spectral graph matching and regularized quadratic relaxations
https://services.math.duke.edu/mcal?abstract-10987
Given two unlabeled, edge-correlated graphs on the same set of vertices, we study the "graph matching" problem of identifying the unknown mapping from vertices of the first graph to those of the second. This amounts to solving a computationally intractable quadratic assignment problem. We propose a new spectral method, which computes eigendecomposition of the two graph adjacency matrices and returns a matching based on the pairwise alignments between all eigenvectors of the first graph with all eigenvectors of the second. Each alignment is inversely weighted by the distance between the corresponding eigenvalues. This spectral method can be equivalently viewed as solving a regularized quadratic programming relaxation of the quadratic assignment problem. We show that for a correlated Erdos-Renyi model, this method can return the exact matching with high probability if the two graphs differ by at most a 1/polylog(n) fraction of edges, both for dense graphs and for sparse graphs with at least polylog(n) average degree. Our analysis exploits local laws for the resolvents of sparse Wigner matrices.
Based on joint work with Zhou Fan, Cheng Mao, Yihong Wu, all at Yale. Preprints available at https://arxiv.org/abs/1907.08880 and https://arxiv.org/abs/1907.08883.Jiaming Xu (Fuqua)2019-09-19T15:15:00-04:0010987probabilityProbability SeminarFall, 2019119 PhysicsThu, 19 Sep 2019 16:15:00 EDTThu, 19 Sep 2019 15:15:00 EDTThursday, September 19, 2019, 3:15pmSatanjeev Banerjee, Software Engineer Research, Twitter
https://services.math.duke.edu/mcal?abstract-10921
Th Sept 19
MLBytes Ahmadieh Grand Hall (GH 330)
4:30 pm (light dinner provided)
Satanjeev Banerjee, TwitterSatanjeev Banerjee (Software Engineer Research, Twitte)2019-09-19T16:30:00-04:0010921Other Meetings and EventsMLBytes WorkshopThu, 19 Sep 2019 16:30:00 EDTThursday, September 19, 2019, 4:30pmThu, 19 Sep 2019 17:30:00 EDTGross Hall, Ahmadieh Family Grand Hall, Room 330Fall, 2019Arjun Devrarjan, Visnu Menon (Toucan AI)
https://services.math.duke.edu/mcal?abstract-10981
Friday Sept 20
Data Dialogue
Arjun Devarajan, Vishnu Menon (Toucan AI)
GH 103 11:45 - 1:00 pmArjun Devrarjan, Visnu Menon (Toucan AI)2019-09-20T11:45:00-04:0010981Data DialogueData DialogueFall, 2019Gross Hall 103Fri, 20 Sep 2019 12:45:00 EDTFri, 20 Sep 2019 11:45:00 EDTFriday, September 20, 2019, 11:45amMoments of half integral weight modular L–functions, bilinear forms and applications
https://services.math.duke.edu/mcal?abstract-11004
Given a half-integral weight holomorphic newform f, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime.
In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan—Petersson conjecture for the form f.
This gives a very sharp Lindelof on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelof hypothesis for such series
was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salie sums. It turns out that such a bilinear form
also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski—Zaharescu.Alexander Dunn (University of Illinois Urbana-Champaign)2019-09-20T14:00:00-04:0011004Number TheoryNumber Theory SeminarFri, 20 Sep 2019 14:00:00 EDTFriday, September 20, 2019, 2:00pmPhysics 047Fri, 20 Sep 2019 15:00:00 EDTFall, 2019The Moduli Space of Matroids
https://services.math.duke.edu/mcal?abstract-10958
I will begin with an introduction to hyperfields (originally introduced by Krasner for number-theoretic reasons), and then discuss a far-reaching generalization, Oliver Lorscheid’s theory of ordered blueprints. Two key examples are the sign hyperfield S and the tropical hyperfield T. I will discuss a common generalization, in this language, of Descartes' Rule of Signs (which involves polynomials over S) and the theory of Newton Polygons (which involves polynomials over T). I will then give a quick introduction to matroids and explain how the theory of ordered blueprints and ordered blue schemes allow us to construct a "moduli space of matroids", which can be viewed as an enhancement of the usual Grassmannian variety in algebraic geometry. This is joint work with Oliver Lorscheid.<a href="http://people.math.gatech.edu/~mbaker/">Matt Baker</a> (Georgia Tech, Mathematics)2019-09-20T15:15:00-04:0010958algebraic geometryNumber TheoryAlgebraic Geometry Seminar119 PhysicsFri, 20 Sep 2019 16:15:00 EDThttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/11026.png" /></div>
Fall, 2019Friday, September 20, 2019, 3:15pmFri, 20 Sep 2019 15:15:00 EDTYesStatic/quasi-static/dynamic models of dislocations: wellposedness and exponential convergence to equilibrium
https://services.math.duke.edu/mcal?abstract-10991
Materials defects such as dislocations are important line defects in crystalline materials and they play essential roles in understanding materials properties like plastic deformation. In this talk, I will first talk about the mathematical validation of the static PN models for both straight and curved dislocation line by establishing the relationship between the PN model in the full space and the reduced problem on the slip plane in terms of both governing equations and energy minimizers. Then we study the relaxation process of dynamic Peierls-Nabarro dislocation model, which is a gradient flow with infinite nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. We will show the dynamic solution will converge exponentially to a shifted steady profile which is uniquely determined.<a href="mailto:yg86@duke.edu">Yuan Gao</a> (Duke University)2019-09-23T12:00:00-04:0010991Graduate-FacultyGraduate/faculty SeminarMon, 23 Sep 2019 13:00:00 EDTPhysics 119Fall, 2019Monday, September 23, 2019, 12:00pmMon, 23 Sep 2019 12:00:00 EDTA refinement of the Lefschetz decomposition for hyperkahler manifolds
https://services.math.duke.edu/mcal?abstract-10999
The cohomology (with complex coefficients) of a compact kahler manifold M admits an action of the algebra sl(2,C), and this action plays an essential role in the analysis of the cohomology. In the case that M is a hyperkahler manifold Verbitsky and Looijenga—Lunts showed there is a family of such sl(2,C)’s generating an algebra isomorphic to so(4,b_2-2), and this algebra similarly can tell us quite a bit about the cohomology of the hyperkahler. I will describe some results of this nature for both the Hodge numbers and Nagai’s conjecture on the nilpotent logarithm of monodromy arising from a degeneration. This is joint work with Mark Green, Radu Laza and Yoonjoo Kim.<a href="https://services.math.duke.edu/~robles/index.html">Colleen Robles</a> (Duke U)2019-09-23T15:15:00-04:0010999geometry/topologyGeometry SeminarFall, 2019119 PhysicsMon, 23 Sep 2019 16:15:00 EDTYesMon, 23 Sep 2019 15:15:00 EDTMonday, September 23, 2019, 3:15pmMulti-Representation Manifold Learning on Fibre Bundles
https://services.math.duke.edu/mcal?abstract-10890
Fibre bundles serve as a natural geometric setting for many learning problems involving non-scalar pairwise interactions. Modeled on a fixed principal bundle, different irreducible representations of the structural group induce many associated vector bundles, encoding rich geometric information for the fibre bundle as well as the underlying base manifold. An intuitive example for such a learning paradigm is phase synchronization---the problem of recovering angles from noisy pairwise relative phase measurements---which is prototypical for a large class of imaging problems in cryogenic electron microscopy (cryo-EM) image analysis. We propose a novel nonconvex optimization formulation for this problem, and develop a simple yet efficient two-stage algorithm that, for the first time, guarantees strong recovery for the phases with high probability. We demonstrate applications of this multi-representation methodology that improve denoising and clustering results for cryo-EM images. This algorithmic framework also extends naturally to general synchronization problems over other compact Lie groups, with a wide spectrum of potential applications.Tingran Gao (University of Chicago)2019-09-25T12:00:00-04:0010890applied math and analysisApplied Math And Analysis SeminarFall, 2019119 PhysicsWed, 25 Sep 2019 13:00:00 EDTWed, 25 Sep 2019 12:00:00 EDTWednesday, September 25, 2019, 12:00pmStochastic and continuum dynamics in cellular transport
https://services.math.duke.edu/mcal?abstract-11062
The cellular cytoskeleton is essential in proper cell function as well as in organism development. These filaments represent the roads along which most protein transport occurs inside cells. I will discuss several examples where questions about filament motor protein interactions require the development of novel mathematical modeling, analysis, and simulation.
In the development of egg cells into embryos, RNA molecules bind to and unbind from cellular roads called microtubules, switching between bidirectional transport, diffusion, and stationary states. Since models of intracellular transport can be analytically intractable, asymptotic methods are useful in understanding effective cargo transport properties as well as their dependence on model parameters. We consider these models in the framework of partial differential equations as well as stochastic processes and derive large time properties of cargo movement for a general class of problems. The proposed methods have applications to macroscopic models of protein localization and microscopic models of cargo movement by teams of motor proteins. I will also discuss an agent-based modeling and data analysis framework for understanding how actin filaments and myosin motors interact to form contractile ring channels essential in development. In particular, we propose tools drawing from topological data analysis to analyze time-series data of filamentous network interactions and illustrate the impact of key parameters on significant hole emergence, thus giving insight into ring channel formation and maintenance.<a href="mailto:ciocanel.1@mbi.osu.edu">Veronica Ciocanel</a> (Ohio State University)2019-09-25T15:15:00-04:0011062applied math and analysisApplied Math And Analysis SeminarFall, 2019119 PhysicsWed, 25 Sep 2019 16:15:00 EDTWednesday, September 25, 2019, 3:15pmWed, 25 Sep 2019 15:15:00 EDTBranching diffusion processes in periodic media
https://services.math.duke.edu/mcal?abstract-10996
We investigate the asymptotic behavior of solutions to parabolic partial differential equations (PDEs) in R^d with space-periodic diffusion matrix, drift, and potential. Using this asymptotics, we describe the behavior of branching diffusion processes in periodic media. In particular, for a super-critical branching process in periodic media, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k−th moment dominates the k−th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge.Pratima Hebbar (Duke)2019-09-26T15:15:00-04:0010996probabilityProbability SeminarThursday, September 26, 2019, 3:15pmThu, 26 Sep 2019 15:15:00 EDTFall, 2019Thu, 26 Sep 2019 16:15:00 EDT119 PhysicsJohn Bralich, Infinia ML
https://services.math.duke.edu/mcal?abstract-10922
9/26/2019
MLBytes Ahmadieh Grand Hall (GH 330)
John Bralich, Infinia MLJohn Bralich (Infinia ML)2019-09-26T16:30:00-04:0010922Other Meetings and EventsMLBytes WorkshopThursday, September 26, 2019, 4:30pmThu, 26 Sep 2019 16:30:00 EDTGross Hall, Ahmadieh Family Grand Hall, Room 330Thu, 26 Sep 2019 17:30:00 EDTFall, 2019Kelsey Sumner, UNC Epidemiology
https://services.math.duke.edu/mcal?abstract-10924
Fri Sep 27, 2019 11:45 am - 1pm
Data Dialogues GH 103
Kelsey Sumner, UNC EpidemiologyKelsey Sumner (UNC Epidemiology)2019-09-27T11:45:00-04:0010924Data DialogueData DialogueGross Hall 103Fri, 27 Sep 2019 13:00:00 EDTFall, 2019Fri, 27 Sep 2019 11:45:00 EDTFriday, September 27, 2019, 11:45amModel theory and complexity
https://services.math.duke.edu/mcal?abstract-11020
The ultraproduct construction in model theory gives a way of averaging an infinite sequence of mathematical structures, such as fields, graphs, or linear orders. The talk will be about the strength of such a construction.<a href="mailto:mem@math.uchicago.edu">Maryanthe Malliaris</a> (University of Chicago)2019-09-27T12:00:00-04:0011020ColloquiumMathematics Colloquium SeminarFall, 2019Physics 130Fri, 27 Sep 2019 13:00:00 EDTFriday, September 27, 2019, 12:00pmFri, 27 Sep 2019 12:00:00 EDTMechanistic models of genetic admixture
https://services.math.duke.edu/mcal?abstract-10926
One of the major insights from the modern genomic era is the ubiquity of migration and admixture throughout human history and the animal kingdom. Admixed populations are formed through the exchange of individuals from two or more previously isolated populations. These processes shape modern human genetic and phenotypic variation, and lead to differences in disease risk between populations. Intricate sociocultural practices such as marriage customs, colonization events, and phenotypic preferences direct how parental populations interact to form admixed human populations. Despite this complexity, previous methods often considered admixed populations as simple linear combinations of their parental populations. Instead, we describe a series of mechanistic models, considering the admixture processes such as sex-specific contributions and nonrandom mating. We demonstrate that previous work misestimates population history parameters, such as the timing and intensity of migration, and may infer admixture histories that are qualitatively different. Under a related framework, we apply the model to human population genetic data to infer human migrations and interactions through time.Amy Goldberg (Duke University, Evolutionary Anthropology)2019-09-27T13:30:00-04:0010926mathematical biologyMathematical Biology SeminarFri, 27 Sep 2019 14:30:00 EDTPhysics 235Fall, 2019Friday, September 27, 2019, 1:30pmFri, 27 Sep 2019 13:30:00 EDTModuli of symmetric cubic fourfolds and nodal sextic curves
https://services.math.duke.edu/mcal?abstract-10877
Period map is a powerful tool to study geometric objects related to K3 surfaces and cubic 4-folds. In this talk, we focus on moduli of cubic 4-folds and sextic curves with specified symmetries and singularities. We identify the geometric (GIT) compactifications with the Hodge theoretic (Looijenga, mostly Baily-Borel) compactifications of locally symmetric varieties. As a corollary, the algebra of GIT invariants is identified with the algebra of automorphic forms on the corresponding period domains. One of the key inputs is the functorial property of semi-toric compactifications of locally symmetric varieties. Our work generalizes results of Matsumoto-Sasaki-Yoshida, Allcock-Carlson-Toledo, Looijenga-Swierstra and Laza-Pearlstein-Zhang. This is joint work with Zhiwei Zheng.<a href="https://www.math.upenn.edu/people/chenglong-yu">Chenglong Yu</a> (U Penn)2019-09-27T15:15:00-04:0010877algebraic geometryAlgebraic Geometry SeminarFall, 2019119 PhysicsFri, 27 Sep 2019 16:15:00 EDTYesFri, 27 Sep 2019 15:15:00 EDTFriday, September 27, 2019, 3:15pmEdge states and topological insulators beyond periodic structures
https://services.math.duke.edu/mcal?abstract-11081
Topological insulators are materials with the property that electrical current flows around their edge in a way that is remarkably robust to imperfections in the material. In the past decade, this behavior has attracted huge attention from physicists and engineers. In this talk I will describe what topological insulators are, what the state of rigorous mathematical understanding of these materials is, and then present my own work, which aims to (1) clarify what happens to edge currents in the presence of imperfections (2) extend some of the current theory of T.I.s to disordered (non-periodic) systems.Alex Watson (Duke University)2019-09-30T12:00:00-04:0011081Graduate-FacultyGraduate/faculty SeminarMonday, September 30, 2019, 12:00pmMon, 30 Sep 2019 12:00:00 EDTMon, 30 Sep 2019 13:00:00 EDT119 PhysicsFall, 2019DGA Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial
https://services.math.duke.edu/mcal?abstract-10970
Given a pattern braid $\beta\in J^1(S^1)$, to any Legendrian knot $\Lambda$ in $\mathbb{R}^3$ with the standard contact structure, we can associate the Legendrian satellite knot $S(\Lambda,\beta)$. We will discuss the relationship between counts of augmentations of the ChekanovEliashberg differential graded algebra of $S(\Lambda,\beta)$ and counts of certain representations of the algebra of $\Lambda$. We will then define an $m$graded $n$colored ruling polynomial from the $m$graded ruling polynomial, analogously to how the $n$colored HOMFLYPT polynomial is
defined from the HOMFLYPT polynomial, and extend results of the second author, to show that the $2$graded $n$colored ruling polynomial appears as a specialization of the $n$colored HOMFLYPT polynomial. This is joint work with Dan Rutherford.<a href="https://sites.google.com/site/caitlinleverson3/">Caitlin Leverson</a> (Georgia Tech)2019-09-30T15:15:00-04:0010970Triangle Topologygeometry/topologyTriangle Topology SeminarFall, 2019Mon, 30 Sep 2019 16:15:00 EDT119 PhysicsMonday, September 30, 2019, 3:15pmMon, 30 Sep 2019 15:15:00 EDTComputational Humanities Reading Group
https://services.math.duke.edu/mcal?abstract-11090
What is digital humanities (DH) and what are the critical frameworks that inform the field? This reading group is meant as an wide ranging exploration of DH and computational methods broadly understood.
For the academic year 2019-2020, the reading group is broadly structured to focus on:
¿ theoretical background in the Fall Semester;
¿ methodological concerns in the Spring Semester
Please click here for more information and a list of readings for the academic year:
https://sites.duke.edu/criticaldh/home/
This reading group is organized with the co-sponsorship of the Rhodes Information Initiative at Duke and the Digital Humanities Initiative at FHI.
Questions? Please contact Prof. Astrid Giugni (astrid.giugni@duke.edu)Astrid Giugni 2019-10-01T17:00:00-04:0011090Other Meetings and EventsTue, 01 Oct 2019 18:00:00 EDTGross Hall 318Fall, 2019Tue, 01 Oct 2019 17:00:00 EDTTuesday, October 1, 2019, 5:00pmAnalysis and computation of nonlocal models
https://services.math.duke.edu/mcal?abstract-10948
Nonlocal models are experiencing a firm upswing recently as more realistic alternatives to the conventional local models for studying various phenomena from physics and biology to materials and social sciences. In this talk, I will describe our recent effort in taming the computational challenges for nonlocal models. I will first highlight a family of numerical schemes -- the asymptotically compatible schemes -- for nonlocal models that are robust with the modeling parameter approaching an asymptotic limit. Second, fast algorithms will be presented to reduce the high computational cost from the numerical implementation of the nonlocal operators. Although new nonlocal models have been gaining popularity in various applications, they often appear as phenomenological models, such as the peridynamics model in fracture mechanics. Here we will try to provide better perspectives of the origin of nonlocality from multiscale modeling and homogenization, which in turn may help the development of more effective numerical methods for homogenization.<a href="mailto:xtian@math.utexas.edu">Xiaochuan Tian</a> (UT Austin)2019-10-02T12:00:00-04:0010948applied math and analysisApplied Math And Analysis Seminar119 PhysicsWed, 02 Oct 2019 13:00:00 EDTFall, 2019Wednesday, October 2, 2019, 12:00pmWed, 02 Oct 2019 12:00:00 EDTYesGradient Flows: From PDE to Data Analysis.
https://services.math.duke.edu/mcal?abstract-11078
Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs. We present recent results on properties of these equilibria and long-time asymptotics of solutions in the setting where attractive and repulsive forces are in competition.
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<a href="mailto:franca.hoffmann@gmail.com">Franca Hoffmann</a> (Caltech)2019-10-02T15:15:00-04:0011078applied math and analysisApplied Math And Analysis SeminarWed, 02 Oct 2019 16:15:00 EDT119 PhysicsFall, 2019Wednesday, October 2, 2019, 3:15pmWed, 02 Oct 2019 15:15:00 EDTYesML@Duke Seminar
https://services.math.duke.edu/mcal?abstract-11088
Recurrent World Models Facilitate Policy Evolution
Abstract: We explore building generative neural network models of popular reinforcement learning environments. Our world model can be trained quickly in an unsupervised manner to learn a compressed spatial and temporal representation of the environment. By using features extracted from the world model as inputs to an agent, we can train a very compact and simple policy that can solve the required task. We can even train our agent entirely inside of its own dream environment generated by its world model, and transfer this policy back into the actual environment.
Links:
https://worldmodels.github.io/
https://papers.nips.cc/paper/7512-recurrent-world-models-facilitate-policy-evolutionCollin Cooke 2019-10-02T16:30:00-04:0011088Other Meetings and EventsWednesday, October 2, 2019, 4:30pmWed, 02 Oct 2019 16:30:00 EDTWed, 02 Oct 2019 17:30:00 EDTGross Hall, Ahmadieh Family Grand Hall, Room 330Fall, 2019An MCMC method with rapid mixing
https://services.math.duke.edu/mcal?abstract-11058
The Metropolis-Hastings method is often used to construct a Markov chain with a given π as its stationary distribution. The method works even if π is known only up to an intractable constant of proportionality. Polynomial time convergence results for such chains (rapid mixing) are hard to obtain for high dimensional probability models where the size of the state space potentially grows exponentially with the model dimension. In a Bayesian context, Yang, Wainwright, and Jordan (2016) (=YWJ) used the path method to prove rapid mixing for high dimensional linear models.
We propose a modification of the YWJ approach that simplifies the theoretical argument and improves the rate of convergence. The new approach is illustrated by an application to an exponentially weighted aggregation estimation.Xiaoqian (Dana) Yang (Duke, Fuqua)2019-10-03T15:15:00-04:0011058probabilityProbability SeminarFall, 2019Thu, 03 Oct 2019 16:15:00 EDT119 PhysicsThursday, October 3, 2019, 3:15pmThu, 03 Oct 2019 15:15:00 EDTTim Sell (K-Lab)
https://services.math.duke.edu/mcal?abstract-10950
Fri Oct 4, 2019 11:45am - 1pm
Data Dialogue GH 103
Tim Sell (K-Lab)Tim Sell (K-Lab)2019-10-04T11:45:00-04:0010950Data DialogueData DialogueFri, 04 Oct 2019 11:45:00 EDTFriday, October 4, 2019, 11:45amFri, 04 Oct 2019 12:45:00 EDTGross Hall 103Fall, 2019Intrinsic complexity: from approximation of random vectors and random fields to solutions of PDEs
https://services.math.duke.edu/mcal?abstract-11034
We characterize the intrinsic complexity of a set in a metric space by the least dimension of a linear space that can approximate the set to a given tolerance. This is dual to the characterization of the set using Kolmogorov n-width, the distance from the set to the best n-dimensional linear space. In this talk I will start with the intrinsic complexity of a set of random vectors (via principal component analysis) and random fields (via Karhunen–Loève expansion) and then characterize solutions to partial differential equations of various type. Our study provides a mathematical understanding of the complexity/richness and its mechanism of the underlying problem independent of representation basis. In practice, our study is directly related to the question of whether there is a low rank approximation to the associated (discretized) linear system, which is essential for dimension reduction and developing fast algorithms.<a href="https://www.math.uci.edu/~zhao/homepage/home/home.html">Hongkai Zhao</a> (University of California, Irvine)2019-10-04T12:00:00-04:0011034ColloquiumMathematics Colloquium Seminarhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/8734.jpg" /></div>
Fall, 2019Fri, 04 Oct 2019 13:00:00 EDT130 PhysicsFriday, October 4, 2019, 12:00pmYesFri, 04 Oct 2019 12:00:00 EDTRigidity of Schubert varieties in rational homogeneous manifolds of Picard number one
https://services.math.duke.edu/mcal?abstract-10909
Given a rational homogeneous manifold S=G/P of Picard number one and a Schubert variety S_0 of S, the pair (S,S_0) is said to be homologically rigid if any subvariety of S having the same homology class as S_0 must be a translate of S_0 by G. The pair (S,S_0) is said to be Schur rigid if any subvariety of S with homology class equal to a multiple of the homology class of S_0 must be a sum of translates of S_0. In this talk we use the theory of minimal rational curves to get homological rigidity and apply a refined form of transversality to reduce Schur rigidity to homological rigidity, proving that (S,S_0) exhibits Schur rigidity whenever S_0 is a non-linear smooth Schubert variety. This is joint work with N. Mok.Jaehyun Hong (Korea Institute for Advanced Study)2019-10-04T15:15:00-04:0010909algebraic geometryAlgebraic Geometry SeminarFriday, October 4, 2019, 3:15pmFri, 04 Oct 2019 15:15:00 EDTFall, 2019119 PhysicsFri, 04 Oct 2019 16:15:00 EDTOn (provably) Learning with Large Neural Networks
https://services.math.duke.edu/mcal?abstract-10903
Virtually all modern deep learning systems are trained with some form of local descent algorithm over a high-dimensional parameter space. Despite its apparent simplicity, the mathematical picture of the resulting setup contains several mysteries that combine statistics, approximation theory and optimization, all intertwined in a curse of dimensionality.
In order to make progress, authors have focused in the so-called 'overparametrised' regime, which studies asymptotic properties of the algorithm as the number of neurons grows. In particular, neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for its favorable training properties. In this regime, gradient descent obeys a deterministic partial differential equation (PDE) that converges to a globally optimal solution for networks with a single hidden layer under appropriate assumptions.
In this talk, we will review recent progress on this problem, and argue that such framework might provide crucial robustness against the curse of dimensionality. First, we will describe a non-local mass transport dynamics that leads to a modified PDE with the same minimizer, that can be implemented as a stochastic neuronal birth-death process, and such that it provably accelerates the rate of convergence in the mean-field limit. Next, such dynamics fit naturally within the framework of total-variation regularization, which following [Bach’17] have fundamental advantages in the high-dimensional regime. We will discuss a unified framework that controls both optimization, approximation and generalisation errors using large deviation principles, and discuss current open problems in this research direction.
Joint work with G. Rotskoff (NYU), and E. Vanden-Eijnden (NYU).Joan Bruna (NYU)2019-10-09T12:00:00-04:0010903applied math and analysisApplied Math And Analysis SeminarWednesday, October 9, 2019, 12:00pmWed, 09 Oct 2019 12:00:00 EDTWed, 09 Oct 2019 13:00:00 EDTGross 330Fall, 2019Low degree points on curves
https://services.math.duke.edu/mcal?abstract-11115
The central problem of arithmetic geometry is to understand the rational solutions to systems of polynomial equations. A first case is when the algebraic variety cut out by the equations has dimension one, i.e., it is a curve. The behavior of the set of rational solutions varies with the topological type of the curve. It is potentially infinite when the genus is small, but is always finite once the genus is at least two by Faltings' theorem.
In this talk we will consider an invariant of a curve measuring how large of an extension of the base field one must allow in order to have infinitely many solutions. This provides an arithmetic analogue of the gonality of the curve and we will explore these two measures of irrationality using geometric techniques.<a href="mailto:vogti@stanford.edu">Isabel Vogt</a> (Stanford University / University of Washington, Mathematics)2019-10-09T15:15:00-04:0011115algebraic geometryAlgebraic Geometry Seminarhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/11114.jpg" /></div>
Fall, 2019Wed, 09 Oct 2019 16:15:00 EDT119 PhysicsWed, 09 Oct 2019 15:15:00 EDTWednesday, October 9, 2019, 3:15pmNon-parametric change point detection in growing networks
https://services.math.duke.edu/mcal?abstract-11044
Motivated by applications of modeling both real world and probabilistic systems such as recursive trees, the last few years have seen an explosion in models for dynamically evolving networks. In this talk, we consider models of growing networks which evolve via new vertices attaching to the pre-existing network according to one attachment function f till the system grows to size τ(n) < n, when new vertices switch their behavior to a different function g till the system reaches size n. We explore the effect of this change point on the evolution and final degree distribution of the network. In particular, we consider two cases, the standard model where τ(n) = γn as well as the quick big bang model when τ(n) = nγ for some 0 < γ < 1. In the former case, we obtain deterministic ‘fluid limits’ to track the degree evolution in the sup-norm metric. In the latter case, we show that the effect of the pre-change point dynamics ‘washes out’ when the network reaches size n, although the maximal degree feels the effect of the change. We also devise non-parametric, consistent estimators to detect the change point. Our methods exploit and develop new techniques connecting inhomogeneous continuous time branching processes (CTBP) to the evolving networks. This is joint work with Shankar Bhamidi and Iain Carmichael.Sayan Banerjee (UNC)2019-10-10T16:15:00-04:0011044probabilityProbability SeminarThu, 10 Oct 2019 17:15:00 EDTat UNC, 125 Hanes HallFall, 2019Thursday, October 10, 2019, 4:15pmThu, 10 Oct 2019 16:15:00 EDTTommy Lin (pondr)
https://services.math.duke.edu/mcal?abstract-10983
Friday October 11, 2019
Data Dialogue
Tommy Lin (pondr)
GH 103
11:45-1:00 pmTommy Lin (pondr)2019-10-11T11:45:00-04:0010983Data DialogueData DialogueFri, 11 Oct 2019 11:45:00 EDTFriday, October 11, 2019, 11:45amGross Hall 103Fri, 11 Oct 2019 12:45:00 EDTFall, 2019Frontiers in Mathematics Lecture 1: Representations of p-adic groups
https://services.math.duke.edu/mcal?abstract-11018
The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of certain matrix groups, called p-adic groups.
In my talk I will introduce p-adic groups and provide an overview of our understanding of their representations, with an emphasis on recent progress. I will also briefly discuss applications to other areas, e.g. to automorphic forms and the global Langlands program.<a href="mailto:fintzen@umich.edu">Jessica Fintzen</a> 2019-10-11T12:00:00-04:0011018Frontiers in MathematicsNumber TheoryFrontiers in Mathematics SeminarFriday, October 11, 2019, 12:00pmYesFri, 11 Oct 2019 12:00:00 EDTFall, 2019Fri, 11 Oct 2019 13:00:00 EDTPhysics 130Gliomas Diagnosis, Progress, and Treatment: A Mathematical Approach
https://services.math.duke.edu/mcal?abstract-10935
The diagnosis and treatment of gliomas continue to pose a significant challenge for oncologists who not only have to contend with managing acute neurological symptoms, but also the almost inevitable development of resistance to treatment. Indeed, the last 25 years have produced minimal advancements in treatment efficacy, even though significant efforts and resources have been invested in the quest for breakthroughs. This effort has not been restricted only to clinicians or oncologists, with mathematical modeling also playing an increasingly important role. The work presented seeks to focus our attention back to the most fundamental question: why are gliomas fatal? Biologically, it is known that glioma lethality is driven by a fast growth that increases intracranial pressure resulting in lethal neurological damage, which current treatments fail to prevent due to tumor cell resistance to treatments such as chemotherapy. The work comprises two main parts: (1) in silico optimization of treatment strategies using chemotherapy coupled with novel cell-repair inhibitors currently in various stages of the clinical trial; and (2) a study of tumor-induced intracranial pressure and edema in gliomas of grade I-IV. Both approaches come together as a first step towards a better understanding of the poor survival rates of patients afflicted with gliomas. They raise new questions about what characterizes the malignancy of primary brain tumors and how clinicians can fight it. Continued modeling effort in these directions has the potential to make an impact in the field of brain cancer diagnostics and treatment.Inmaculada Sorribes (Duke University, Mathematics)2019-10-11T13:30:00-04:0010935mathematical biologyMathematical Biology SeminarPhysics 235Fri, 11 Oct 2019 14:30:00 EDTFall, 2019Fri, 11 Oct 2019 13:30:00 EDTFriday, October 11, 2019, 1:30pmLocal Multiplicity for Spherical Varieties
https://services.math.duke.edu/mcal?abstract-10956
In this talk, I will discuss the local multiplicity problem for spherical varieties. I will start with the conjecture of Sakellaridis and Venkatesh. Then I will discuss the behavior of the multiplicity over the local L-packet. Finally I will explain how to use the trace formula method to study the multiplicity.<a href="mailto:chenwan@mit.edu">Chen Wan</a> (MIT)2019-10-11T15:15:00-04:0010956Number TheoryNumber Theory Seminar119 PhysicsFri, 11 Oct 2019 16:15:00 EDTFall, 2019Fri, 11 Oct 2019 15:15:00 EDTFriday, October 11, 2019, 3:15pmEuler numbers in A^1-homotopy theory
https://services.math.duke.edu/mcal?abstract-10905
(jt. with Kirsten Wickelgren)
Given a cohomology theory for (smooth) algebraic varieties, we explain
how to use the motivic six functors formalism to associate Euler classes
(and Euler numbers) to vector bundles over smooth (and proper)
varieties, valued in the cohomology theory. Using more properties of the
six functors formalism, in the presence of a non-degenerate section we
can compute the Euler number in terms of certain local contributions
around the zeros, called indices. We then relate the indices to certain
A^1-degrees, and also to the so-called Scheja-Storch form.
This generalizes, but is independent of, other results of Kass-Wickelgren.<a href="http://tom-bachmann.com/">Tom Bachmann</a> (Massachusetts Institute of Technology, Mathematics)2019-10-14T15:15:00-04:0010905geometry/topologyGeometry/topology SeminarFall, 2019Mon, 14 Oct 2019 16:15:00 EDTPhysics 119Monday, October 14, 2019, 3:15pmMon, 14 Oct 2019 15:15:00 EDTPlanar surface embeddings and non-convex harmonic maps
https://services.math.duke.edu/mcal?abstract-11125
Mappings between domains are among the most basic and versatile tools used in the computational analysis and manipulation of shapes. Their applications range from animation in computer graphics to analysis of anatomical variation and anomaly detection in medicine and biology.
My talk will start with a brief overview of discrete computational shape mapping, surface parameterization (flattening), and their applications. I will then discuss invertibility, an often desirable property of mappings, and present an optimization approach for efficiently computing invertible surface maps. With large-scale problems in mind, we will focus on Tutte’s embedding theorem and its continuous counterpart, the Rado-Kneser-Choquet theorem: they assert that planar harmonic maps (solutions of Laplace’s equation) with convex boundary conditions are invertible. Finally, we will see that convexity, a key ingredient of both theorems, can be replaced with a novel, less restrictive and geometrically intuitive condition, thus extending these theorems to the case of harmonic maps onto non-convex domains.<a href="mailto:shaharko@math.duke.edu">Shahar Kovalsky</a> (Duke University, Mathematics)2019-10-16T12:00:00-04:0011125applied math and analysisApplied Math And Analysis SeminarWednesday, October 16, 2019, 12:00pmWed, 16 Oct 2019 12:00:00 EDTFall, 2019Wed, 16 Oct 2019 13:00:00 EDT119 PhysicsLong time dynamics for two dimensional water waves
https://services.math.duke.edu/mcal?abstract-11113
The water wave equations describe the motion of the free surface of a fluid (e.g. water) under the action of various physical forces.
Understanding the long time properties of water wave flows is a very interesting yet also very challenging class of problems. The talk will provide an overview of recent and ongoing work in this direction.Mihaela Ifrim (UW-Madison)2019-10-16T15:15:00-04:0011113applied math and analysisApplied Math And Analysis SeminarWed, 16 Oct 2019 15:15:00 EDTWednesday, October 16, 2019, 3:15pmFall, 2019119 PhysicsWed, 16 Oct 2019 16:15:00 EDTRandom Additions in Urns of Integers
https://services.math.duke.edu/mcal?abstract-11001
Consider an urn containing balls labeled with integer values. Define a process by drawing two balls, observing the values, then replacing the balls in the urn along with a new ball labeled with the sum of the two drawn balls. What does the configuration of the urn look like after many rounds? The surprising result is an exponential limit law for the empirical distribution defined by the urn. The mean is a random variable which depends on the starting configuration. I will outline the proof of convergence, which uses the contraction method for recursive distributional equations. I will also discuss some other interesting urn models that include the features of multi-drawing and an infinite type of balls.Mackenzie Simper (Stanford statistics)2019-10-17T15:15:00-04:0011001probabilityProbability Seminar119 PhysicsThu, 17 Oct 2019 16:15:00 EDTFall, 2019Thu, 17 Oct 2019 15:15:00 EDTThursday, October 17, 2019, 3:15pmPeter Baumgartner (RTI)
https://services.math.duke.edu/mcal?abstract-11008
Friday October 25
Data Dialogue GH 103 11:45 - 1:00 pm
Peter Baumgartner (RTI)Peter Baumgartner (RTI)2019-10-18T11:45:00-04:0011008Data DialogueData DialogueFri, 18 Oct 2019 11:45:00 EDTFriday, October 18, 2019, 11:45amFri, 18 Oct 2019 12:45:00 EDTGross Hall 103Fall, 2019Cell cycle synchronization in early Drosophila embryos
https://services.math.duke.edu/mcal?abstract-11095
Early embryogenesis of most metazoans is characterized by rapid and synchronous cleavage divisions. While diffusion is too slow for synchronization of mitosis across large spatial scales, traveling waves represent a possible process of synchronization. I will discuss our recent work dissecting the molecular and physical mechanisms for the generation of traveling waves of activity of Cdk1, the master regulator of the cell cycle. I will show that the in vivo dynamics of Cdk1 are captured by a transiently bistable reaction-diffusion model, where time-dependent reaction terms account for the growing level of cyclins and Cdk1 activation across the cell cycle. I will discuss two distinct regimes. The first one is observed in mutants of the mitotic switch. There, waves are triggered by the classical mechanism of a stable state invading a metastable one. Conversely, waves in wild type reflect a transient phase that preserves the Cdk1 spatial gradients while the overall level of Cdk1 activity is swept upward by the time-dependent reaction terms. This unique mechanism generates a wave-like spreading (sweep-waves) that differs from bistable waves for its dependence on dynamic parameters and its faster speed. I will also discuss how the integration of biochemical and mechanical processes is required for the early establishment of synchronization of the cell cycle.Stefano Di Talia (Duke University, Cell Biology)2019-10-18T13:30:00-04:0011095mathematical biologyMathematical Biology SeminarFriday, October 18, 2019, 1:30pmFri, 18 Oct 2019 13:30:00 EDTFall, 2019235 PhysicsFri, 18 Oct 2019 14:30:00 EDTLecture 2: From representations of p-adic groups to congruences of automorphic forms
https://services.math.duke.edu/mcal?abstract-10952
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.
This is joint work with Sug Woo Shin.
Reception to follow at 4:30pm.Jessica Fintzen (University of Cambridge)2019-10-18T15:15:00-04:0010952Frontiers in MathematicsNumber TheoryFrontiers in Mathematics SeminarFriday, October 18, 2019, 3:15pmFri, 18 Oct 2019 15:15:00 EDTFall, 2019Fri, 18 Oct 2019 16:15:00 EDT119 PhysicsHilbert's Generalized Third Problem and the Algebraic K-theory of Fields
https://services.math.duke.edu/mcal?abstract-11055
In this talk I'll explain how one might attack Hilbert's Generalized Third Problem via homotopy theory. Two n-dimensional polytopes, $P$, $Q$ are said to be scissors congruent if one can cut $P$ along a finite number of hyperplanes, and re-assemble the pieces into $Q$. The scissors congruence problem, aka Hilbert Generalized Third Problem, asks: when can we do this? what obstructs this? In two dimensions, two polygons are scissors congruent iff they have the same area. In three dimensions, there is volume AND another invariant, the Dehn Invariant. In higher dimensions, very little is known. I'll give an introduction to this very classical problem, and explain how homotopy theory can be used to get purchase on it. Prerequisites: The discussion of Hilbert's Third Problem and Dehn's invariant will be widely accessible. No knowledge of algebraic K-theory will be assumed. This is all joint work with Inna Zakharevich.Jonathan Campbell (Duke University)2019-10-21T12:00:00-04:0011055Graduate-FacultyGraduate/faculty Seminar119 PhysicsMon, 21 Oct 2019 13:00:00 EDTFall, 2019Monday, October 21, 2019, 12:00pmMon, 21 Oct 2019 12:00:00 EDTGap and index estimates for Yang-Mills and harmonic map theory
https://services.math.duke.edu/mcal?abstract-10974
In this talk we want to discuss joint work with Streets and Gursky on two related questions about the variational structure of the Yang-Mills functional in dimension four. The first is the question of ‘gap’ estimates; i.e., determining an energy threshold below which any solution must be an instanton, hence a minimizer for the Y-M energy. The second question is about non-minimal solutions, and in this case the problem is to estimate the index of a solution. Time permitting, we will also discuss related joint work with Gursky on a gap estimate in harmonic map theory.Casey Lynn Kelleher (Princeton)2019-10-21T15:15:00-04:0010974geometry/topologyGeometry/topology SeminarMon, 21 Oct 2019 15:15:00 EDTMonday, October 21, 2019, 3:15pmFall, 2019Mon, 21 Oct 2019 16:15:00 EDT119 PhysicsPLUM: A mathematician goes to court: Understanding Gerrymandering
https://services.math.duke.edu/mcal?abstract-11096
This a story of both mathematics informing the law AND legal questions suggesting new mathematical problems. How does one identify and understand gerrymandering? Can we really recognize gerrymandering when we see it? If one party wins over 50% of the vote is it fair that it wins less than 50% of the seats? What do we mean by fair? How can math help illuminate these questions? For me these question began with a Duke Math PRUV undergraduate research program project in 2013, continued through a sequence of iiD Data+ projects, and has lead me to testify twice in two cases. Common Cause v. Rucho went to the US Supreme court and Common Cause v. Lewis resulted, just last month, in the redrawing of the NC State Legislative district maps. The legal discussion has been informed by the mathematical frame work, but the problem of understanding gerrymandering has also prompted the development of a number of new computational algorithms which come with new mathematical questions.<a href="mailto:jonm@math.duke.edu">Jonathan Mattingly</a> (Duke University, Mathematics)2019-10-21T16:30:00-04:0011096Public LecturesPublic Lectures SeminarMonday, October 21, 2019, 4:30pmMon, 21 Oct 2019 16:30:00 EDTFall, 2019https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10771.jpg" /></div>
128 PhysicsMon, 21 Oct 2019 17:30:00 EDTThe times they are a-changin
https://services.math.duke.edu/mcal?abstract-11122
Sparsity-based methods for inverse problems gained widespread popularity in the 2000s when compressed-sensing theory provided groundbreaking insights on sparse recovery from randomized measurements. However, this theory does not explain the empirical success of sparse-recovery techniques in problems where the measurements are deterministic and structured. In the first half of this talk we will present a theory of sparse recovery for deterministic measurement operators relevant to optics, electroencephalography, quantitative magnetic-resonance imaging, and signal processing. In the second half we will illustrate the potential of deep neural networks in this domain with an application to super-resolution of line spectra. Deep learning techniques achieve remarkable empirical performance for a variety of inverse problems, but the mechanisms they implement are shrouded in mystery. We will conclude by showing that a local linear-algebraic analysis of a network trained for image denoising makes it possible to visualize some of the learned mechanisms, and reveals intriguing connections to traditional methodology.Carlos Fernandez-Granda (Assistant Professor of Mathematics and Data Science)2019-10-22T11:45:00-04:0011122Other Meetings and EventsSpecial Seminar in Machine Learning and Optimization Optimization methods for inverse problemsFall, 2019Gross Hall 324Tue, 22 Oct 2019 12:45:00 EDTTue, 22 Oct 2019 11:45:00 EDTTuesday, October 22, 2019, 11:45amBeyond Arnold’s geodesic framework of an ideal hydrodynamics
https://services.math.duke.edu/mcal?abstract-10553
In the talk we discuss ramifications of Arnold’s
group-theoretic approach to ideal hydrodynamics as the geodesic flow
for a right-invariant metric on the group of volume-preserving
diffeomorphisms. We show that problems of optimal mass transport are
in a sense dual to the Euler hydrodynamics. Moreover, many equations
of mathematical physics, such as the motion of vortex sheets or fluids
with moving boundary, have Lie groupoid, rather than Lie group,
symmetries (this is a joint work with Anton Izosimov).Boris Khesin (U of Toronto)2019-10-23T12:00:00-04:0010553applied math and analysisApplied Math And Analysis SeminarWed, 23 Oct 2019 13:00:00 EDTPhysics 119Fall, 2019Wednesday, October 23, 2019, 12:00pmWed, 23 Oct 2019 12:00:00 EDTKnot concordance and 4-manifolds
https://services.math.duke.edu/mcal?abstract-11024
There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will highlight some historical and recent connections between knot concordance (a weak notion of equivalence for knots) and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth structures. I will also discuss a new method for using 4-manifolds to study knot concordance, and use it to show that the Conway knot is not slice.
Reception to follow at 4:30.Lisa Piccirillo (Brandeis University / Massachusetts Institute of Technology)2019-10-23T15:15:00-04:0011024Frontiers in Mathematicsgeometry/topologyFrontiers In Mathematics SeminarWed, 23 Oct 2019 15:15:00 EDTWednesday, October 23, 2019, 3:15pmFall, 2019Wed, 23 Oct 2019 16:15:00 EDTPhysics 119Sensing, Signals, and Communication Seminar with Jean-Francois Chamberland, Texas A&M
https://services.math.duke.edu/mcal?abstract-11038
Coding and Compressed Sensing for Unsourced Multiple Access
Currently deployed wireless access systems based on sustained connectivity, channel estimates, and scheduling policies are ill-equipped to deal with the sporadic traffic generated by legions of unattended wireless devices. This impending technological challenge has fueled several recent research initiatives whose shared goal is to ready wireless infrastructures for the demands of tomorrow. Pertinent recent advances in this area include the introduction of unsourced, uncoordinated multiple-access models attuned to machine-driven communications and the assessment of their fundamental limits for messages with small payloads. This presentation will review recent contributions on this topic and focus on a novel communication scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent progress in compressed sensing and forward error correction to produce a novel uncoordinated access paradigm, along with a computationally efficient decoding algorithm. Within this framework, every active device partitions its data into several sub-blocks and, subsequently, adds redundancy using a systematic linear block code. Compressed sensing techniques are then employed to recover sub-blocks up to a permutation of their order, and the original messages are obtained by stitching fragments together using a tree-based algorithm.Jean-Francois Chamberland (Texas A&M)2019-10-24T11:45:00-04:0011038Other Meetings and EventsFall, 2019Thu, 24 Oct 2019 12:45:00 EDTGross Hall 318Thursday, October 24, 2019, 11:45amThu, 24 Oct 2019 11:45:00 EDTConstructing extremal stationary distributions for the Voter Model in $d\geq 3$ as factors of IID
https://services.math.duke.edu/mcal?abstract-10993
The Voters Model in $\mathbb{Z}^d$ lattice is a well studied interacting particle system. For $d \geq 3$, it has a one parameter family of extremal stationary distributions. Steif and Tykesson asked if these stationary distributions are factors of IID, or equivalently, isomorphic to Bernoulli shifts. We give an affirmative answer to this question. Our result also gives the first natural example of the so-called divide and color models, such that each cluster of the partition is infinite, while the coloring process is a factor of IID.
It is a joint work with Allan Sly.<a href="https://arxiv.org/abs/1908.09450">Lingfu Zhang</a> (Princeton)2019-10-24T15:15:00-04:0010993probabilityProbability SeminarThursday, October 24, 2019, 3:15pmThu, 24 Oct 2019 15:15:00 EDTFall, 2019119 PhysicsThu, 24 Oct 2019 16:15:00 EDTAlex Sigman & Kabir Seth, Dow Jones
https://services.math.duke.edu/mcal?abstract-11014
Thursday October 24
MLBytes Ahmadieh Grand Hall (GH 330)
Alex Sigman and Kabir Seth, Dow JonesAlex Sigman & Kabir Seth (Dow Jones)2019-10-24T16:30:00-04:0011014Other Meetings and EventsMLBytes WorkshopFall, 2019Thu, 24 Oct 2019 17:30:00 EDTGross Hall, Ahmadieh Family Grand Hall, Room 330Thursday, October 24, 2019, 4:30pmThu, 24 Oct 2019 16:30:00 EDTJascha Swisher, Laboratory of Analytic Sciences
https://services.math.duke.edu/mcal?abstract-11030
October 25, 2019
Data Dialogue
Jascha Swisher, Laboratory of Analytic Sciences
GH 103
11:45-1:00 pmJascha Swisher (Laboratory of Analytic Sciences)2019-10-25T09:00:00-04:0011030Data DialogueData DialogueFriday, October 25, 2019, 9:00amFri, 25 Oct 2019 09:00:00 EDTFall, 2019Fri, 25 Oct 2019 10:00:00 EDTGross Hall 103Knot traces and PL embeddings
https://services.math.duke.edu/mcal?abstract-11025
It is still at the forefront of 4-manifold topology to produce (algebraically) small 4-manifolds which admit exotic smooth structures. Knot traces are 4-manifolds built by attaching a (thickened) disk to B^4; these fundamental manifolds are smooth and homotopy equivalent to S^2. We build smooth 4-manifolds which are homeomorphic to a knot trace but not diffeomorphic to any knot trace; this shows that knot traces can even admit an exotic smooth structure with fundamentally distinct Morse theory. As a corollary, we show that there are smooth 4-manifolds homotopy equivalent to a genus g surface such that there is no PL embedding of the surface that realizes the homotopy equivalence. This gives a new proof of Lidman-Levine’s recent solution to problem 4.25 on Kirby’s list. This is joint work in progress with Kyle Hayden.Lisa Piccirillo (Brandeis University / Massachusetts Institute of Technology)2019-10-25T12:00:00-04:0011025Frontiers in Mathematicsgeometry/topologyFrontiers In Mathematics SeminarFriday, October 25, 2019, 12:00pmFri, 25 Oct 2019 12:00:00 EDTFri, 25 Oct 2019 13:00:00 EDTPhysics 119Fall, 2019Tissue structure accelerates evolution: premalignant sweeps precede neutral expansion
https://services.math.duke.edu/mcal?abstract-11065
Recent debate on tumor heterogeneity has largely centered on the presence (or absence) of subclonal selection. While neutral and Darwinian models of tumor evolution have both been shown to recapitulate bulk sequencing data, multi-region sequencing has produced evidence supporting the hypothesis that early Darwinian selection precedes late neutral evolution after malignant transformation. Transitioning modes of evolution (Darwinian to neutral) may be the outcome of cellular architecture dictating spatial constraints for growth. Using a classic, well-studied computational model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This novel model extension represents biologically realistic scale (1e6 – 1e7 cells) in a biologically realistic setting (3-dimensional breast ductal network derived from imaging data) of premalignancy. The branching topology of ductal networks at tumor initiation determines two important evolutionary accelerants: spatial constraints and cellular dispersal. This model approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects.Jeffrey West (H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology)2019-10-25T13:30:00-04:0011065mathematical biologyMathematical Biology SeminarFri, 25 Oct 2019 13:30:00 EDTFriday, October 25, 2019, 1:30pmFri, 25 Oct 2019 14:30:00 EDT235 PhysicsFall, 2019Picard ranks of reductions of K3 surfaces over global fields
https://services.math.duke.edu/mcal?abstract-10964
For a K3 surface X over a number field with potentially good reduction everywhere, we prove that there are infinitely many primes modulo which the reduction of X has larger geometric Picard rank than that of the generic fiber X. A similar statement still holds true for ordinary K3 surfaces over global function fields. In this talk, I will present the proofs via the intersection theory on GSpin Shimura varieties and also discuss various applications. These results are joint work with Ananth Shankar, Arul Shankar, and Salim Tayou and with Davesh Maulik and Ananth Shankar.<a href="mailto:yunqingt@math.Princeton.EDU">Yunqing Tang</a> (Princeton University)2019-10-25T15:15:00-04:0010964Number TheoryNumber Theory SeminarFri, 25 Oct 2019 15:15:00 EDTYesFriday, October 25, 2019, 3:15pm119 PhysicsFri, 25 Oct 2019 16:15:00 EDTFall, 2019https://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10963.jpg" /></div>
Determining Risk Factors for Triple Whammy Acute Kidney Injury: Sex-specific Modeling and Analysis
https://services.math.duke.edu/mcal?abstract-11124
Concurrent use of a diuretic, a renin-angiotensin system (RAS) inhibitor,
and a nonsteroidal anti-inflammatory drug (NSAID) significantly increases
the risk of acute kidney injury (AKI). This phenomenon is known as 'triple
whammy'. Diuretics and RAS inhibitors, such as an angiotensin converting
enzyme inhibitor (ACEI) or angiotensin receptor blocker (ARB), are often
prescribed in tandem for the treatment of hypertension, whereas some NSAIDs,
such as ibuprofen, are available over the counter. As such, concurrent
treatment with all three drugs is not uncommon. The goals of this study are
to better understand the mechanisms underlying the development of triple
whammy AKI and to identify physiological factors that may increase an
individual's susceptibility. To accomplish these goals, we utilize
computational models of long-term blood pressure regulation. We found that
individual variation in water intake or the myogenic response as well as
high dosages of these drugs may predispose triple whammy patients to develop AKI. The computational models used
include variables describing the heart and circulation, kidney function,
sodium and water reabsorption in the nephron and the RAS, and are
parameterized separately for men and women.<a href="https://math.duke.edu/people/jessica-leete">Jessica Leete</a> (Duke University, Mathematics)2019-10-25T15:30:00-04:0011124Graduate-FacultyGraduate/faculty Seminar, special SIAM-AWM Graduate Student TalkFri, 25 Oct 2019 16:30:00 EDTPhysics 235Fall, 2019Fri, 25 Oct 2019 15:30:00 EDTFriday, October 25, 2019, 3:30pmKoszul duality and Knot Floer homology
https://services.math.duke.edu/mcal?abstract-10915
‘Koszul duality’ is a phenomenon which algebraists are fond of, and has previously been studied in the context of '(bordered) Heegaard Floer homology' by Lipshitz, Ozsváth and Thurston. In this talk, I shall discuss an occurrence of Koszul duality which links older constructions in Heegaard Floer homology with the bordered Heegaard Floer homology of three-manifolds with torus boundary. I shan’t assume any existing knowledge of Koszul duality or any form of Heegaard Floer homology.Tom Hockenhull (University of Glasgow, Mathematics)2019-10-28T15:15:00-04:0010915Triangle Topologygeometry/topologyTriangle Topology SeminarMonday, October 28, 2019, 3:15pmMon, 28 Oct 2019 15:15:00 EDT119 PhysicsMon, 28 Oct 2019 16:15:00 EDTFall, 2019Summaries of persistence diagrams and their applications
https://services.math.duke.edu/mcal?abstract-11016
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to be challenging as the space is complicated. For that reason, transforming these diagrams in a way that is compatible with machine learning is an important topic currently researched in TDA. In this talk, we propose two summaries: persistence statistics and persistence curves. To demonstrate their effectivenesses, their applications to sleep stage analysis (joint work with Hau-Tieng Wu, and Yu-Lun Lo), and texture classification (joint work with Austin Lawson), will be presented. The stability property will also be discussed.Yu-Min Chung (UNC)2019-10-30T12:00:00-04:0011016applied math and analysisApplied Math And Analysis SeminarFall, 2019Wed, 30 Oct 2019 13:00:00 EDT119 PhysicsWed, 30 Oct 2019 12:00:00 EDTWednesday, October 30, 2019, 12:00pmExploring moduli spaces in complex dynamics
https://services.math.duke.edu/mcal?abstract-11022
A major goal in complex dynamics is to understand "dynamical moduli spaces"; that is, conformal conjugacy classes of holomorphic dynamical systems. One of the great successes in this regard is the study of the moduli space of quadratic polynomials; it is isomorphic to $\mathbb C$. This moduli space contains the famous Mandelbrot set, which has been extensively studied over the past 40 years. Understanding other dynamical moduli spaces to the same extent tends to be more challenging as they are often higher-dimensional. In this talk, we will begin with an overview of complex dynamics, focusing on the moduli space of quadratic rational maps, which is isomorphic to $\mathbb C^2$. We will explore this space, finding many interesting objects along the way.
Note: special tea at 2:45.<a href="mailto:kochsc@umich.edu">Sarah Koch</a> (University of Michigan)2019-10-30T15:15:00-04:0011022ColloquiumMathematics Colloquium SeminarFall, 2019Physics 119Wed, 30 Oct 2019 16:15:00 EDTYesWed, 30 Oct 2019 15:15:00 EDTWednesday, October 30, 2019, 3:15pmA Gentle Introduction to Crystalline Cohomology
https://services.math.duke.edu/mcal?abstract-10994
Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can be described as the solutionsto a system of polynomial equations). Grothendieck showed that the de Rham cohomology of X can be computed using only polynomial differential forms on X. This observation was the starting point for the theory of algebraic de Rham cohomology, which has proved to be a useful invariant for algebraic varieties over an arbitrary field k. In the case where k has positive characteristic, Berthelot and Grothendieck introduced a refinement of algebraic de Rham cohomology, known as crystalline cohomology. In this talk, I will review the theory of algebraic de Rham cohomology and sketch an elementary construction of crystalline cohomology, based on recent joint work with Bhargav Bhatt and Akhil Mathew.<a href="https://www.ias.edu/scholars/lurie">Jacob Lurie</a> (IAS, Mathematics)2019-10-31T15:00:00-04:0010994ColloquiumGraduate-Sponsored ColloquiumThu, 31 Oct 2019 15:00:00 EDTThursday, October 31, 2019, 3:00pmThu, 31 Oct 2019 16:00:00 EDT130 PhysicsFall, 2019Kevin Branin, Rodrigo Silva (IBM)
https://services.math.duke.edu/mcal?abstract-11042
Friday November 1
Data Dialogue
Kevin Branin, Rodrigo Silva (IBM)
GH 103 11:45 - 1:00 pmKevin Branin, Rodrigo Silva (IBM)2019-11-01T11:45:00-04:0011042Data DialogueData DialogueFriday, November 1, 2019, 11:45amFri, 01 Nov 2019 11:45:00 EDTFall, 2019Gross Hall 103Fri, 01 Nov 2019 12:45:00 EDTAdaptation and selection during residual disease and tumor recurrence
https://services.math.duke.edu/mcal?abstract-11067
Tumor recurrence following therapy is the leading cause of death in many cancer types, including some of the most common epithelial tumors such as breast and prostate cancer. Many breast tumors recur more than 5 years after initial surgery and treatment, and recurrences as long as 20 years following therapy have been documented. This has led to the suggestion that a population of tumor cells – referred to as minimal residual disease – can survive treatment and persist in a dormant, clinically undetectable state for years or even decades. These dormant residual cells are the likely reservoir for disease recurrence. Because recurrent breast cancer is generally incurable, developing strategies to forestall recurrence by therapeutically targeting residual cells during the dormant stage is of paramount importance. While recent work in this area has focused on specific pathways that promote the survival and recurrence of dormant cells, several fundamental questions about dormancy have not yet been addressed: How does the clonal composition of tumors change during dormancy and recurrence? Is tumor recurrence driven by the selection of a subset of dormant residual cells? Do dormant tumor cells undergo adaptive changes that allow them to recur? Because primary breast tumors are be heterogeneous, harboring different subclones of (epi)genetically distinct cells, it is likely that dormancy and recurrence are accompanied by profound changes in the clonal composition of tumors. However, the clonal dynamics of these processes has not been examined, due in part to the difficulty in studying dormant residual disease in humans. We are using a validated mouse model of breast cancer dormancy and recurrence to study clonal evolution during residual disease and recurrence. To do this, we are taking a cellular barcoding approach, which allows us to directly assess, on a single-cell level, how the clonal composition of tumors changes during dormancy and recurrence. Importantly, combining barcoding with this genetically engineered mouse model can provide novel insights that could not be found using other approaches.James Alvarez (Duke University, Pharmacology and Cancer Biology)2019-11-01T13:30:00-04:0011067mathematical biologyMathematical Biology SeminarFriday, November 1, 2019, 1:30pmFri, 01 Nov 2019 13:30:00 EDT235 PhysicsFri, 01 Nov 2019 14:30:00 EDTFall, 2019A Riemann-Hilbert Correspondence in Characteristic p
https://services.math.duke.edu/mcal?abstract-10954
Let k be a perfect field of characteristic p, and let Gal(k) denote the absolute Galois group of k. By a classical result of Katz, the category of finite-dimensional F_p-vector spaces with an action of Gal(k) is equivalent to the category of finite-dimensional k-vector spaces with a Frobenius-semilinear automorphism. In this talk, I'll discuss some joint work with Bhargav Bhatt which generalizes Katz's result, replacing the field k by an arbitrary F_p-scheme X. In this case, there is a correspondence relating p-torsion etale sheaves on X to quasi-coherent sheaves on X equipped with a Frobenius-semilinear automorphism, which can be viewed as a "mod p" version of the Riemann-Hilbert correspondence for complex algebraic varieties.Jacob Lurie (IAS)2019-11-01T15:15:00-04:0010954algebraic geometryAlgebraic Geometry SeminarFriday, November 1, 2019, 3:15pmFri, 01 Nov 2019 15:15:00 EDT119 PhysicsFri, 01 Nov 2019 16:15:00 EDTFall, 2019Solving eigenvalue problem using neural network
https://services.math.duke.edu/mcal?abstract-11140
Solving high-dimensional eigenvalue problems have been difficult for a long time due to the curse of dimensionality. In recent years, neural networks have been proved to be efficient in high dimensional function approximations because of their compositional structures. In our work, we introduce a power method to solve eigenvalue problems. Starting from BSDE formulation, we represent the eigenfunction and its scaled gradient with two neural networks. Then, a least-squares objective function is designed for parameter optimizations. Numerical results of a variety of examples show that our algorithm is accurate in high-dimensions.Mo Zhou (Duke University)2019-11-04T12:00:00-05:0011140Graduate-FacultyGraduate/faculty SeminarMonday, November 4, 2019, 12:00pmMon, 04 Nov 2019 12:00:00 ESTFall, 2019119 PhysicsMon, 04 Nov 2019 13:00:00 ESTScalar curvature and circle-valued harmonic maps
https://services.math.duke.edu/mcal?abstract-10946
We introduce a new tool for relating the scalar curvature of a Riemannian manifold to its global geometry and topology, based on the study of level sets of harmonic functions and harmonic maps to the circle. We will explain how these ideas lead to simple new proofs and improvements upon some well-known results in three-manifold geometry and general relativity, previously studied primarily via minimal surface and Dirac operator methods.<a href="mailto:stern.daniel.l@gmail.com">Daniel Stern</a> (University of Toronto)2019-11-04T15:15:00-05:0010946geometry/topologyGeometry/topology SeminarYesMon, 04 Nov 2019 15:15:00 ESTMonday, November 4, 2019, 3:15pmFall, 2019119 PhysicsMon, 04 Nov 2019 16:15:00 ESTSpecial Lecture on Math+Data+Health and Beyond
https://services.math.duke.edu/mcal?abstract-11056
Today's technological world is increasingly dependent upon the reliability, robustness, quality of service and timeliness of networks including those of power distribution, financial, transportation, communication, biological, and social. For the time-critical functionality in transferring resources and information, a key requirement is the ability to adapt and reconfigure in response to structural and dynamic changes, while avoiding disruption of service and catastrophic failures. We will outline some of the major problems for the development of the necessary theory and tools that will permit the understanding of network dynamics in a multiscale manner.
Many interesting networks consist of a finite but very large number of nodes or agents that interact with each other. The main challenge when dealing with such networks is to understand and regulate the collective behavior. Our goal is to develop mathematical models and optimization tools for treating the Big Data nature of large scale networks while providing the means to understand and regulate the collective behavior and the dynamical interactions (short and long-range) across such networks.
The key mathematical technique will be based upon the use optimal mass transport theory and resulting notions of curvature applied to weighted graphs in order to characterize network robustness. Examples will be given from biology, finance, and transportation.Allen Tannenbaum 2019-11-06T11:45:00-05:0011056Other Meetings and EventsWednesday, November 6, 2019, 11:45amWed, 06 Nov 2019 11:45:00 ESTFall, 2019Gross Hall, Ahmadieh Family Grand Hall, Room 330Wed, 06 Nov 2019 12:45:00 ESTNonlinear PDEs and graph-based learning
https://services.math.duke.edu/mcal?abstract-10892
This talk will focus on recent connections between PDEs and regularization in graph-based learning. We will discuss graph-based semi-supervised learning, where graph Laplacian regularization is widely used. In the limit of vanishingly few labels, Laplacian learning is a discretization of an ill-posed PDE and gives poor results. We present a new rigorous analysis of this ill-posedness using random walks on graphs, and will also discuss new models for regularization in graph based learning that are provably well-posed with very few labels, and have connections to nonlinear elliptic PDEs, including the p-Laplace equation. We will also present some new results on error estimates for spectral convergence of the graph Laplacian to the Laplace-Beltrami operator on the data manifold that use a unique blend of variational methods and PDE techniques.Jeff Calder (University of Minnesota)2019-11-06T12:00:00-05:0010892applied math and analysisApplied Math And Analysis SeminarWednesday, November 6, 2019, 12:00pmWed, 06 Nov 2019 12:00:00 EST119 PhysicsWed, 06 Nov 2019 13:00:00 ESTFall, 2019Likelihood-based Inference for Stochastic Epidemic Models with application to High-resolution Contact Tracking Data
https://services.math.duke.edu/mcal?abstract-11142
Stochastic epidemic models such as the Susceptible-Infectious-Removed (SIR) model are widely used to model the spread of disease at the population level, but fitting these models poses significant challenges when missing data or latent variables are present. In particular, the likelihood function has long been considered intractable in such settings. We will discuss our recent work using generating function techniques that newly enable likelihood computations without model simplifications in the presence of missing infection and recovery times. Motivated by a study of influenza transmission with social contact tracking data, we then present a data-augmented MCMC algorithm for fitting parameters of the SIR model when the underlying contact network evolves continuously. This co-evolution entails interdependence between individuals' disease statuses and social contacts through time. We demonstrate that accounting for the contact network and epidemic dynamics jointly is crucial for valid inference, and apply the method to analyze data from the eX-FLU study of influenza on a college campus.Jason Xu (Assistant Professor of Statistical Science, Duke University)2019-11-06T15:30:00-05:0011142Machine LearningMachine Learning SeminarWed, 06 Nov 2019 15:30:00 ESTWednesday, November 6, 2019, 3:30pmGross Hall, Ahmadieh Family Grand Hall, Room 330Wed, 06 Nov 2019 16:30:00 ESTFall, 2019A new universality class for critical percolation on networks with heavy-tailed degrees
https://services.math.duke.edu/mcal?abstract-10930
A new universality class for critical percolation on networks with heavy-tailed degrees
Abstract: The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdős-Rényi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment.
In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far.
This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden.Souvik Dhara (MIT)2019-11-07T16:15:00-05:0010930probabilityProbability SeminarFall, 2019Thu, 07 Nov 2019 17:15:00 ESTat UNC, 125 Hanes HallThursday, November 7, 2019, 4:15pmThu, 07 Nov 2019 16:15:00 ESTLeslie DeJesus
https://services.math.duke.edu/mcal?abstract-11061
TH Nov. 7
ML Bytes GH 330
Leslie DeJesusLeslie DeJesus 2019-11-07T16:30:00-05:0011061Other Meetings and EventsMLBytes WorkshopThu, 07 Nov 2019 16:30:00 ESTThursday, November 7, 2019, 4:30pmFall, 2019Gross Hall, Ahmadieh Family Grand Hall, Room 330Thu, 07 Nov 2019 17:30:00 ESTRajneesh Patil (Iqvia)
https://services.math.duke.edu/mcal?abstract-11077
Friday November 8
Data Dialogues
Rajneesh Patil (Iqvia)
11:45 - 1:00
GH 103Rajneesh Patil (Iqvia)2019-11-08T11:45:00-05:0011077Data DialogueData DialogueGross Hall 103Fri, 08 Nov 2019 12:45:00 ESTFall, 2019Friday, November 8, 2019, 11:45amFri, 08 Nov 2019 11:45:00 ESTRatiometric signaling and directional sensing in yeast
https://services.math.duke.edu/mcal?abstract-11146
Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations across the cell. Nevertheless, the tiny cells of the yeast Saccharomyces cerevisiae reliably decode gradients of extracellular pheromones to find their mates. We will describe recent work, using both experimental imaging and mathematical modeling, to understand how this is possible, even when the pheromone receptor density is uneven across the cell. An important observation is that during an initial polarization phase, yeast cells appear to respond to the fraction of occupied receptors rather than simply the concentration of ligand-bound receptors. The talk will be based on a recent joint work with colleagues at Duke and UNC: Nicholas T. Henderson, Michael Pablo, Debraj Ghose, Manuella R. Clark-Cotton, Trevin R. Zyla, and Timothy C. Elston.Jim Nolen and Daniel Lew 2019-11-08T13:30:00-05:0011146mathematical biologyMathematical Biology SeminarFri, 08 Nov 2019 13:30:00 ESTFriday, November 8, 2019, 1:30pmFall, 2019235 PhysicsFri, 08 Nov 2019 14:30:00 ESTModuli spaces of sheaves on K3 surfaces and Galois representations
https://services.math.duke.edu/mcal?abstract-10939
Moduli spaces of sheaves on K3 surfaces have been well-studied when defined over the complex numbers, because they are one of the known families of hyperkaehler varieties. However, many of their arithmetic properties when defined over an arbitrary field are still unknown. In this talk, I will tell you about a new result in this direction: two such moduli spaces of the same dimension, when defined over a finite field, have the same number of points defined over every finite field extension of the base field, which is surprising when the moduli spaces are not birational. The way to get at this result is to study the cohomology groups of the moduli spaces as Galois representations. Over an arbitrary field, we find that all of the cohomology groups are isomorphic as Galois representations.<a href="https://pages.uoregon.edu/sfrei/">Sarah J Frei</a> (U Oregon)2019-11-08T15:15:00-05:0010939algebraic geometryAlgebraic Geometry SeminarFall, 2019119 PhysicsFri, 08 Nov 2019 16:15:00 ESTFriday, November 8, 2019, 3:15pmYesFri, 08 Nov 2019 15:15:00 ESTYet another proof that Alexander polynomial one knots are topologically slice
https://services.math.duke.edu/mcal?abstract-10884
This proof leverages Freedman's construction showing that any integer homology sphere bounds a contractible topological 4-manifold and is joint work with JungHwan Park and Peter Teichner.<a href="http://people.mpim-bonn.mpg.de/aruray/">Arunima Ray</a> (Max Planck Institute for Mathematics)2019-11-11T15:15:00-05:0010884Triangle Topologygeometry/topologyTriangle Topology SeminarMonday, November 11, 2019, 3:15pmMon, 11 Nov 2019 15:15:00 ESThttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10883.jpg" /></div>
Fall, 2019119 PhysicsMon, 11 Nov 2019 16:15:00 ESTAn example of anomalous dissipation for passive scalars
https://services.math.duke.edu/mcal?abstract-11006
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars.
We give an example of a rough divergence-free velocity field that explicitly exhibits anomalous dissipation for passive scalars.
The mechanism for scalar dissipation is a built-in direct energy cascade in the synthetic velocity field.
Connections to the Obukhov–Corrsin monofractal theory of scalar turbulence will be discussed.Theodore Drivas (Princeton University)2019-11-13T12:00:00-05:0011006applied math and analysisApplied Math And Analysis SeminarWed, 13 Nov 2019 12:00:00 ESTWednesday, November 13, 2019, 12:00pmPhysics 119Wed, 13 Nov 2019 13:00:00 ESTFall, 2019Recent advances on the loop-erased walk
https://services.math.duke.edu/mcal?abstract-11084
The loop-erased walk is the process obtained be erasing loops chronologically from a simple random walk. It is closely related to a number of processes including uniform spanning trees. I will give a survey of recent (last five years or so) progress on this process obtained with a number of co-authors. I will try to make this talk accessible at a “colloquium” level.Greg Lawler (Chicago)2019-11-14T15:15:00-05:0011084probabilityProbability SeminarThu, 14 Nov 2019 15:15:00 ESTThursday, November 14, 2019, 3:15pmFall, 2019119 PhysicsThu, 14 Nov 2019 16:15:00 ESTAnalysis and geometry of free boundaries: recent developments
https://services.math.duke.edu/mcal?abstract-11101
In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation (PDE)), and a set where this function has a specific behavior. Two central issues in the study of free boundary problems and related problems in the calculus of variations and geometric measure theory are: <br/>
(1) What is the optimal regularity of the solution u? <br/>
(2) How smooth is the free boundary (or how smooth is a certain set related to u)? <br/>
In this talk, I will overview recent developments in obstacle type problems and, time permitting, almost minimizers of Bernoulli-type functionals, illustrating techniques that can be used to tackle questions (1) and (2) in various settings. <br/>
The study of the classical obstacle problem - one of the most renowned free boundary problems - began in the ’60s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. Nowadays obstacle type problems continue to offer many challenges and their study is as active as ever.
While the classical obstacle problem arises from a minimization problem (as many other PDEs do), minimizing problems with noise lead to the notion of almost minimizers. Interestingly, though deeply connected to "standard" free boundary problems, almost minimizers do not satisfy a PDE as minimizers do, requiring additional tools from geometric measure theory to address (1) and (2).<a href="mailto:Mariana.SmitVegaGarcia@wwu.edu">Mariana Smit Vega Garcia</a> (Western Washington University)2019-11-15T12:00:00-05:0011101applied math and analysisApplied Math And Analysis SeminarFri, 15 Nov 2019 13:00:00 ESTPhysics 119Fall, 2019Fri, 15 Nov 2019 12:00:00 ESTIntFriday, November 15, 2019, 12:00pmCancer overdiagnosis – a discourse on population health, biologic mechanism and statistics
https://services.math.duke.edu/mcal?abstract-11148
In this talk we discuss the issue of cancer overdiagnosis and overtreatment as a multi-scale problem at the interface of cancer biology, population health and patient preferences. We highlight recent parallel developments in the fields of cancer biology and population-based estimation of overdiagnosis, and we argue that effective approaches to the problem of overdiagnosis and overtreatment requires approaches that integrate evidence from different spatio-temporal scales.Marc D. Ryser 2019-11-15T13:30:00-05:0011148mathematical biologyMathematical Biology SeminarFriday, November 15, 2019, 1:30pmFri, 15 Nov 2019 13:30:00 ESTFall, 2019Fri, 15 Nov 2019 14:30:00 EST235 PhysicsOn motivic Donaldson-Thomas theory on the local projective plane
https://services.math.duke.edu/mcal?abstract-11012
Donaldson-Thomas (DT) theory is an enumerative theory which counts ideal sheaves of curves on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory is a categorification of the DT theory. This categofication contains more refined information of the moduli space, just like the topological space or cohomology contains more information than an Euler characteristic. In this talk, I will give a brief introduction to motivic DT theory. I will also discuss some results on this theory for moduli spaces of sheaves on the local projective plane.<a href="mailto:yunshi2@illinois.edu">Yun Shi</a> 2019-11-15T15:15:00-05:0011012algebraic geometryAlgebraic Geometry SeminarPhysics 119Fri, 15 Nov 2019 16:15:00 ESTFall, 2019Fri, 15 Nov 2019 15:15:00 ESTFriday, November 15, 2019, 3:15pmStratified MCMC Sampling for Non-Reversible Dynamics
https://services.math.duke.edu/mcal?abstract-11138
Stratified MCMC sampling is an effective tool for analyzing complex
probability distributions, particularly when studying tails, distributions
with many wells or distributions on manifolds. However, while it is
not entirely constrained to reversible systems, integration of stratified
sampling with highly irreversible processes is still limited, especially
considering the advantages that irreversibility often has regarding
sampling speed. Here I will outline a newly proposed stratified algorithm
specifically geared towards irreversible Markov chains, and sketch
my approach to proving convergence and analyzing performance. I will
also outline potential applications, and a possible connection between
the analysis of such stratified methods and the theory of Poisson
equations.Gabe Earle (Duke University)2019-11-18T12:00:00-05:0011138Graduate-FacultyGraduate/faculty SeminarMon, 18 Nov 2019 13:00:00 EST119 PhysicsFall, 2019Monday, November 18, 2019, 12:00pmMon, 18 Nov 2019 12:00:00 ESTCounting embedded curves in symplectic 6-manifolds
https://services.math.duke.edu/mcal?abstract-10872
The number of embedded pseudo-holomorphic curves in a symplectic manifold typically depends on the choice of an almost complex structure on the manifold and so does not lead to a symplectic invariant. However, I will discuss two instances in which such naive counting does define a symplectic invariant, which turns out to be related to the Gopakumar-Vafa conjecture inspired by string theory. The talk is based on joint work with Thomas Walpuski.Aleksander Doan (Columbia/Cambridge)2019-11-18T15:15:00-05:0010872geometry/topologyGeometry/topology SeminarMon, 18 Nov 2019 15:15:00 ESTMonday, November 18, 2019, 3:15pmFall, 2019119 PhysicsMon, 18 Nov 2019 16:15:00 ESTDesigns: a fun Mix of Analysis, Combinatorics and Graph/Number/Spectral Theory
https://services.math.duke.edu/mcal?abstract-11102
Spherical Designs are sets of points on the sphere
with the property that the average of a low-degree polynomial
over the points is the same as the average on the sphere. They
are classical yet full of mysteries; the moment we consider
the problem on other manifolds, we run into Analytic Number
Theory and PDEs. In what came as a surprise, the definition
can be suitably interpreted to make sense on a Graph as well.
The arising structures are breathtaking (I have pictures).
As it turns out, they are naturally related to Extremal Combinatorics
where classical Theorems (Erdos-Ko-Rado, Deza-Frankl, ...)
suddenly turn into beautiful special cases of these "Graphical
Designs". I promise beautiful pictures and many open problems.<a href="mailto:stefan.steinerberger@gmail.com">Stefan Steinerberger</a> (Yale University)2019-11-20T15:15:00-05:0011102Frontiers in Mathematicsapplied math and analysisFrontiers In Mathematics SeminarWed, 20 Nov 2019 15:15:00 ESTWednesday, November 20, 2019, 3:15pmPhysics 119Wed, 20 Nov 2019 16:15:00 ESTFall, 2019Probabilistic reasoning and decision theory under imperfect recall
https://services.math.duke.edu/mcal?abstract-11086
When one cannot remember everything that happened before, how should one form beliefs and make decisions? Examples such as the Sleeping Beauty and Absentminded Driver scenarios provide some insight and can be used to rule out some candidate theories. Nevertheless, at this point, multiple (belief formation theory, decision theory) pairs appear to survive as reasonable candidates. I will give our motivation for caring about these problems from an AI perspective, introduce some of the examples, and briefly describe our work on these topics. No previous background required. Parts of this are joint work with Andrew Critch, Scott Emmons (former UNC undergrad / Robertson Scholar), and Caspar Oesterheld (current Duke CS Ph.D. student).Vincent Conitzer 2019-11-21T15:15:00-05:0011086probabilityProbability SeminarThu, 21 Nov 2019 15:15:00 ESTThursday, November 21, 2019, 3:15pmFall, 2019Thu, 21 Nov 2019 16:15:00 EST119 PhysicsDaniel Egger, Executive in Residence, Duke Master of Engineering Management Program
https://services.math.duke.edu/mcal?abstract-11120
Friday November 22, 2019
Data Dialogue
Daniel Egger
GH 103 11:45-1:00 pmDaniel Egger (Executive in Residence, Duke Master of Engineering Management Program)2019-11-22T11:45:00-05:0011120Data DialogueData DialogueFri, 22 Nov 2019 11:45:00 ESTFriday, November 22, 2019, 11:45amFall, 2019Fri, 22 Nov 2019 12:45:00 ESTGross Hall 103Wasserstein Distance between Point Sets and the Lebesgue Measure
https://services.math.duke.edu/mcal?abstract-11103
We describe some recent results regarding the Wasserstein
distance between specific sets of points and the Lebesgue measure.
This can be understood as a measure of regularity; we describe a
Fourier-analytic perspective that allows us to connect to Analytic
Number Theory. We revisit the old problem of Numerical Integration
of Lipschitz function in the unit cube and refine a 1959 result that
was considered sharp. These problems have a funky interpretation:
if you are trying to open a coffee shop chain, then you have to start
with a few shops at first and then expand. This means the first store
should be centrally located; by induction, the first N stores that you
open should be well-distributed (with regards to the measure of the
coffee-drinking population). Joint work with Louis Brown.<a href="mailto:stefan.steinerberger@gmail.com">Stefan Steinerberger</a> (Yale University)2019-11-22T12:00:00-05:0011103Frontiers in Mathematicsapplied math and analysisFrontiers In Mathematics SeminarFriday, November 22, 2019, 12:00pmFri, 22 Nov 2019 12:00:00 ESTFri, 22 Nov 2019 13:00:00 EST119 PhysicsFall, 2019Forecasting Cancer: Predicting Individual Responses to Intermittent Androgen Deprivation Therapy in Prostate Cancer
https://services.math.duke.edu/mcal?abstract-11069
Intermittent androgen deprivation therapy (IADT) is an attractive treatment approach for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off has been shown to limit toxicities and reduce cumulative dose. While IADT has been shown to delay the development of treatment resistance, underlying mechanisms and actionable biomarkers are required to accurately predict when resistance will emerge and how to maximally delay time to progression. We developed a quantitative framework to simulate the enrichment of prostate cancer stem cell dynamics during treatment as a plausible mechanism of resistance evolution. Using simulated dynamics of cancer stem cells and non-stem cancer cells, we derive longitudinal blood serum prostate-specific antigen (PSA) concentrations that were calibrated to and validated with data of 70 patients undergoing multiple cycles of IADT. Model analysis suggests that cancer stem cell proliferation patterns correlate with PSA dynamics and patient outcomes. Learning these dynamics adaptively from the earlier treatment cycles in individual patients can predict the evolution of resistance in subsequent IADT cycles with a predictive power of 90%, which warrants prospective evaluation in a clinical setting. The model is used to simulate and predict alternative treatment options. In particular, simulations show that response dynamics from the first IADT cycle can be used to identify patients who would benefit from concurrent docetaxel.Renee Brady (Moffitt Cancer Center, Integrated Mathematical Oncology)2019-11-22T13:30:00-05:0011069mathematical biologyMathematical Biology SeminarFriday, November 22, 2019, 1:30pmFri, 22 Nov 2019 13:30:00 ESTFri, 22 Nov 2019 14:30:00 EST235 PhysicsFall, 2019Topological reconstruction theorems for algebraic varieties
https://services.math.duke.edu/mcal?abstract-11040
I will report on joint work in progress with János Kollár, Martin Olsson, and Will Sawin on topological
reconstruction theorems for algebraic varieties. Our results include a universal Torelli theorem of Bogomolov-Tschinkel type, valid for all smooth proper varieties over arbitrary fields. Over the complex numbers, we seem to have uncovered a basic and surprising
property of algebraic geometry: proper normal varieties are uniquely determined as schemes by their Zariski topological spaces. Among other things, this yields a topological version of the classical Gabriel-Rosenberg reconstruction theorem, where the category
of coherent sheaves is replaced by the category of constructible abelian étale sheaves. It also raises various other questions that I will discuss if there is time.
All of these results rest on a strengthening of the classical Veblen-Young fundamental theorem of projective geometry.
In modern language, the original theorem (dating to 1917) roughly says that the full linear structure of a projective space is determined by knowing the underlying point set and the subsets that are lines. Our strengthening shows that it is enough to only
know most of the lines (where "most" has different meanings for finite and infinite fields). In this sense, classical projective geometry appears to exert an unexpected influence on modern algebraic geometry.Max Lieblich 2019-11-22T15:15:00-05:0011040algebraic geometryAlgebraic Geometry SeminarFri, 22 Nov 2019 15:15:00 ESTFriday, November 22, 2019, 3:15pmhttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/11039.jpg" /></div>
Fall, 2019Physics 119Fri, 22 Nov 2019 16:15:00 ESTGeometric flows of $G_2$ structures
https://services.math.duke.edu/mcal?abstract-10966
We will start by discussing a flow of isometric $G_2$ structures. We consider the negative gradient flow of the energy functional restricted to the class of $G_2$ structures inducing a given Riemannian metric. We will discuss various analytic aspects of the flow including global and local derivative estimates, a compactness theorem and a monotonicity formula for the solutions. After defining an entropy functional we will prove that low entropy initial data lead to solutions that exist for all time and converge smoothly to a $G_2$ structure with divergence free torsion. We will also discuss finite time singularities and the singular set of the solutions. Finally, we will discuss the isometric flow "coupled” with the Ricci flow of the underlying metric, which again is a flow of $G_2$ structures, and discuss some of its properties. This is a based on two separate joint works with Panagiotis Gianniotis (University of Athens) and Spiro Karigiannis (University of Waterloo).<a href="https://www.math.uwaterloo.ca/~s2dwived/">Shubham Dwivedi</a> (University of Waterloo, Pure Mathematics)2019-11-25T15:15:00-05:0010966geometry/topologyGeometry/topology SeminarMonday, November 25, 2019, 3:15pmMon, 25 Nov 2019 15:15:00 ESTYesMon, 25 Nov 2019 16:15:00 EST119 PhysicsFall, 2019The isoperimetric inequality on a minimal surface
https://services.math.duke.edu/mcal?abstract-11163
The isoperimetric inequality is one of the most fundamental
results in geometry. A longstanding conjecture asserts that the sharp
isoperimetric inequality should hold on any minimal surface in Euclidean
space. This was confirmed by Carleman for 2D minimal surfaces
diffeomorphic to disks. Since then, various other partial results were
established (mainly in the 2D case). In this lecture, I will present a
proof of this conjecture which works in any dimension and in
co-dimension at most 2. Our proof also gives a sharp version of the
Michael-Simon Sobolev inequality.<a href="mailto:sbrendle@gmail.com">Simon Brendle</a> (Columbia)2019-11-26T12:00:00-05:0011163geometry/topologyGeometry/topology Seminar119 PhysicsTue, 26 Nov 2019 13:00:00 ESTFall, 2019Tue, 26 Nov 2019 12:00:00 ESTTuesday, November 26, 2019, 12:00pmConcordance of light bulbs
https://services.math.duke.edu/mcal?abstract-10886
In 2017, Gabai proved the light bulb theorem: if R and R' are 2-spheres in a 4-manifold X which are homotopic and have a common dual (i.e. R and R' are “light bulbs”), then (modulo a statement about 2-torsion in \pi_1(X)), they are smoothly isotopic. (This setting is motivated by handle cancellation of smooth cobordisms of 4-manifolds.) Schwartz later showed that this 2-torsion hypothesis is necessary, and Schneiderman and Teichner then gave an obstruction in the form of an invariant fq associated to a pair of homotopic spheres that vanishes on light bulbs if and only if they are isotopic.
I consider 2-spheres R and R’ in a 4-manifold $X$ which are homotopic, but when only $R$ has a dual (i.e. R and R’ are “algebraic light bulbs”). In this setting, I prove that R and R’ are smoothly concordant with the same 2-torsion hypothesis as Gabai -- in general, they need not be isotopic. (This setting is motivated by handle cancellation of topological cobordisms of 4-manifolds.) I will talk about this work as well as current joint work with Michael Klug redefining fq to prove that this invariant vanishes on algebraic light bulbs if and only if they are concordant.<a href="https://web.math.princeton.edu/~maggiem/">Maggie Miller</a> (Princeton University, Mathematics)2019-12-02T15:15:00-05:0010886Triangle Topologygeometry/topologyTriangle Topology Seminar119 PhysicsMon, 02 Dec 2019 16:15:00 ESTFall, 2019Monday, December 2, 2019, 3:15pmMon, 02 Dec 2019 15:15:00 ESTDepartment Faculty Meeting
https://services.math.duke.edu/mcal?abstract-11126
Department Faculty meeting<a href="mailto:jonm@math.duke.edu">Jonathan Mattingly</a> (Duke University, Mathematics)2019-12-04T15:15:00-05:0011126Other Meetings and EventsFaculty Meetinghttps://services.math.duke.edu/mcal_files/<div class="frb"><img src="/mcal_files/10771.jpg" /></div>
Fall, 2019119 PhysicsWed, 04 Dec 2019 16:15:00 ESTWednesday, December 4, 2019, 3:15pmWed, 04 Dec 2019 15:15:00 ESTThe contact process on Galton-Watson trees
https://services.math.duke.edu/mcal?abstract-11133
Abstract: The contact process describes an epidemic model where each infected individual recovers at rate 1 and infects its healthy neighbors at rate $\lambda$. We show that for the contact process on Galton-Watson trees, when the offspring distribution (i) is subexponential the critical value for local survival $\lambda_2=0$ and (ii) when it is Geometric($p$) we have $\lambda_2 \le C_p$, where the $C_p$ are much smaller than previous estimates. This is based on an improved (and in a sense sharp) understanding of the survival time of the contact process on star graphs. Recently it is proved by Bhamidi, Nam, Nguyen and Sly (2019) that when the offspring distribution of the Galton-Watson tree has exponential tail, the first critical value $\lambda_1$ of the contact process is strictly positive. We prove that if the contact process survives then the number of infected sites grows exponentially fast. As a consequence we show that the contact process dies out at the critical value $\lambda_1$ and does not survive strongly at $\lambda_2$. Based on joint work with Rick Durrett.Zoe Huang (Duke)2019-12-05T16:15:00-05:0011133probabilityProbability SeminarThursday, December 5, 2019, 4:15pmThu, 05 Dec 2019 16:15:00 EST125 Hanes Hall UNCThu, 05 Dec 2019 17:15:00 ESTFall, 2019Homeostasis-Bifurcation Singularities and Hepatic Lipid Dynamic
https://services.math.duke.edu/mcal?abstract-11179
In this talk I will discuss two separate projects. The projects lie on
opposite ends of the math-biology spectrum with the first being math
inspired by biology and the second being a biological modeling project.
The first project studies the interaction of homeostasis and
bifurcation. Homeostasis can be studied by restricting one’s attention
to homeostasis points—points at which a component of a dynamical system
has a vanishing derivative with respect to a parameter. In a
feed-forward network, if a node has a homeostasis point, downstream
nodes will inherit it. This is the case except when the downstream node
has a bifurcation point coinciding with the homeostasis point. At these
homeostasis-bifurcation points, the downstream node often exhibits
complex behavior as the input parameter is varied. In the case of steady
state bifurcation, this includes multiple homeostatic plateaus separated
by hysteretic switches, which are observed in glycolysis. In the case of
Hopf Bifurcation, the downstream node often has homeostatic limit
cycles, which are observed in circadian rhythms. The second project is
work done during an internship in the quantitative systems pharmacology
group at Pfizer. I will discuss the role of mathematical modeling at
Pfizer and my work on a model for hepatic lipid dynamics. The model is
being developed to better understand how to treat non-alcoholic fatty
liver disease, which affects 30% of adults in the U.S..William Duncan (Duke University, Mathematics)2019-12-06T13:30:00-05:0011179mathematical biologyMathematical Biology SeminarFri, 06 Dec 2019 14:30:00 EST235 PhysicsFall, 2019Fri, 06 Dec 2019 13:30:00 ESTFriday, December 6, 2019, 1:30pmp-adic dynamics of Hecke operators on modular curves
https://services.math.duke.edu/mcal?abstract-10960
The action of Hecke operators in the complex topology, ranges from easy density arguments, to deep equidistribution results due to Duke, Clozel-Ullmo and others. Passing from archimedean to non-archimedean primes raises many interesting questions. I will first explain several good motivations to study this problem, coming both from geometry (stratifications of Shimura varieties) and from arithmetic (properties of singular moduli). I will report on joint work with P. Kassaei (King’s college) on the dynamics of Hecke operators acting on modular curves, considered in the p-adic topology. I will also mention work of Hererro, Menares and Rivera-Letelier and, to the extent time allows, work in progress by the union of these two teams.<a href="mailto:eyal.goren@mcgill.ca">Eyal Goren</a> (McGill University)2019-12-06T14:00:00-05:0010960Number TheoryNumber Theory SeminarFri, 06 Dec 2019 14:00:00 ESTFriday, December 6, 2019, 2:00pmFall, 2019Fri, 06 Dec 2019 15:15:00 EST259 PhysicsThe Radiative Uniqueness Conjecture for Bubbling Wave Maps
https://services.math.duke.edu/mcal?abstract-11181
One of the most fundamental questions in partial differential equations is that of regularity and the possible breakdown of solutions. We will discuss this question for solutions to a canonical example of a geometric wave equation; energy critical wave maps. Break-through works of Krieger-Schlag-Tataru, Rodnianski-Sterbenz and Rapha ̈el-Rodnianski produced examples of wave maps that develop singularities in finite time. These solutions break down by concentrating energy at a point in space (via bubbling a harmonic map) but have a regular limit, away from the singular point, as time approaches the final time of existence. The regular limit is referred to as the radiation. This mechanism of breakdown occurs in many other PDE including energy critical wave equations, Schro ̈dinger maps and Yang-Mills equations. A basic question is the following:
• Can we give a precise description of all bubbling singularities for wave maps with the goal of finding the natural unique continuation of such solutions past the singularity?
In this talk, we will discuss recent work (joint with J. Jendrej and A. Lawrie) which is the first to directly and explicitly connect the radiative component to the bubbling dynamics by constructing and classifying bubbling solutions with a simple form of prescribed radiation. Our results serve as an important first step in formulating and proving the following Radiative Uniqueness Conjecture for a large class of wave maps: every bubbling solution is uniquely characterized by it’s radiation, and thus, every bubbling solution can be uniquely continued past blow-up time while conserving energy.<a href="mailto:caseyrod@mit.edu">Casey Rodriguez</a> (MIT)2019-12-13T12:15:00-05:0011181applied math and analysisApplied Math And Analysis SeminarFriday, December 13, 2019, 12:15pmYesFri, 13 Dec 2019 12:15:00 ESTFall, 2019Fri, 13 Dec 2019 13:15:00 EST119 PhysicsReal roots of random functions
https://services.math.duke.edu/mcal?abstract-11185
Random functions are linear combinations of deterministic functions using independent random coefficients. These innocent-looking objects appear naturally in physics and approximation theory and remain mysterious despite decades of intensive research. We will discuss recent progress on the study of random functions and present our approach via the local universality method to study questions on the real roots. Among the applications, we derive a sharp bound on the mean number of real roots for the Kac polynomial which confirms a conjecture by Kac in 1943. We will also discuss the mean, variance, and the limiting distribution of the number of real roots for several classes of random functions.
This talk is based on several joint papers with Mei-Chu Chang, Yen Do, Hoi Nguyen, and Van Vu.<a href="mailto:hoangoanhmw@gmail.com">Oanh Nguyen</a> (Princeton University)2019-12-16T12:15:00-05:0011185probabilityProbability SeminarMon, 16 Dec 2019 13:15:00 EST119 PhysicsFall, 2019Mon, 16 Dec 2019 12:15:00 ESTIntMonday, December 16, 2019, 12:15pmDepartment [DELETED]
https://services.math.duke.edu/mcal?abstract-12979
Dept. Faculty Meeting 2024-03-22T10:30:00-04:0012979Department of MathematicsR.BryantFriday, March 22, 2024, 10:30amFri, 22 Mar 2024 10:30:00 EDTdeletedFri, 22 Mar 2024 11:30:00 EDTPhysics 119Spring, 2024TBA [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 13:30:00 EDTFriday, March 29, 2024, 1:30pmSpring, 2024Zoom linkFri, 29 Mar 2024 14:30:00 EDTdeletedTBA [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 SeminarIntWed, 10 Apr 2024 15:15:00 EDTWednesday, April 10, 2024, 3:15pmSpring, 2024Wed, 10 Apr 2024 15:15:00 EDTPhysics 119deletedTBA [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 SeminardeletedSpring, 2024Physics 119Tue, 23 Apr 2024 16:15:00 EDTTuesday, April 23, 2024, 3:15pmTue, 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, 2024OnsiteSat, 11 May 2024 14:00:00 EDTdeletedSat, 11 May 2024 11:00:00 EDTSaturday, May 11, 2024, 11:00am