## Department of Mathematics, Duke University

Upcoming Seminars:
• Monday, March 2, 2020, 12:00pm, 119 Physics, Graduate/faculty Seminar
TBD
Shan Shan (Duke University)

• Monday, March 2, 2020, 3:15pm, Physics 119, Geometry/topology Seminar
Cable knots are not thin
Subhankar Dey (University of Buffalo, Mathematics)

Thurston's geometrization conjecture and its subsequent proof for Haken manifolds distinguish knots in S^3 by the geometries in the complement of the knots. While the definition of alternating knots make use of nice knot diagrams, Knot Floer homology, a knot invariant toolbox, defined by Ozsvath-Szabo and Rasumussen, generalizes the definition of alternating knots in the context of knot Floer homology and defines family of quasi-alternating knots which contains all alternating knots. Using Lipshitz-Ozsvath-Thurston's bordered Floer homology, we prove a partial affirmation of a folklore conjecture in knot Floer theory, which bridges these two viewpoints of looking at knots.

• Tuesday, March 3, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Jun Kitagawa (Michigan State University)

• Wednesday, March 4, 2020, 3:15pm, Physics 119, Number Theory Seminar
Arithmetic loci of étale rank $1$ local systems
Helene Esnault (Freie Universitat Berline and IAS)

I’ll give our definition of them, in analogy to Simpson's bialgebraicity notion over the complex numbers, explain what special properties they have, and mention some corollaries (notably hard Lefschetz in rank $1$ in positive characteristic). Joint with Moritz Kerz

• Thursday, March 5, 2020, 4:15pm, at UNC, 125 Hanes Hall, Probability Seminar
Epidemics on Evolving Graphs
Dong Yao (Duke, math)

The evoSIR model is a modification of the usual SIR process on a graph $G$ in which $S-I$ connections are broken at rate $\rho$ and the $S$ connects to a randomly chosen vertex. The evoSI model is the same as evoSI but recovery is impossible. In a 2018 DOMath project the critical value for evoSIR was computed and simulations showed that when $G$ is an Erd\"os-Renyi graph with mean degree 5 the system has a discontinuous phase transition, i.e., as the infection rate $\lambda$ decreases to $\lambda_c$, the final fraction of infected individuals does not converge to 0. In this paper we study evoSI and evoSIR dynamics on graphs generated by the configuration model. We show that for each model there is a quantity $\Delta$ determined by the first three moments of the degree distribution, so that the transition is discontinuous if $\Delta>0$ and continuous if $\Delta<0$. We can also compute the limiting epidemic size in the supercritical regime. In evoSI there is a formula. In evoSIR we have to numerically solve a pair of ODE.

• Friday, March 6, 2020, 11:45am, Gross Hall 103, Data Dialogue
Greg Appelbaum (DIBS)
Greg Appelbaum

Dr. Appelbaum is a member of the Brain Stimulation Division of Psychiatry, where he heads the Human Performance Optimization lab (Opti Lab) and directs the Brain Stimulation Research Center. As a member of the Duke Institute for Brain Sciences (DIBS) he teaches and advises in the Neuroscience major, is an affiliate of the Center for Cognitive Neuroscience, and has a secondary appointment in the Department of Psychology and Neuroscience. Lunch: 11:45 am Seminar: 12:00 noon Professor Appelbaum's research is focused on understanding the psychological and neural mechanisms that support human visual cognition and understanding how these change with experience, rehabilitation, and training. This research has utilized behavioral psychometrics and multiple complimentary human neuroimaging (e.g. fMRI, EEG, fNIRS) and neurostimulation (e.g. TMS, ECT) techniques to understand the complex interplay of perception, attention, memory and motor control. As a faculty, he research has been continually funded by grant awards from DARPA, NIH, and the Army Research Office, leading to over 50 published articles and book sections.

• Monday, March 9, 2020, 3:15pm, Physics 119, Geometry/topology Seminar
Types of lines and Euler Numbers enriched in GW(k)
Sabrina Pauli (University of Oslo)

Motivated by Morel's degree in A1-homotopy theory which takes values in the Grothendieck-Witt ring of a field k, Kass and Wickelgren define the Euler number of an oriented vector bundle valued in GW(k) to be the sum of local A1-degrees of the zeros of a generic section. Using this definition they get an enriched count of lines on a smooth cubic surface in GW(k). In my talk I will compute several Euler numbers valued in GW(k). In particular, I will count lines on quintic threefolds. In addition, I will give a geometric interpretation of the local contribution of a line on a quintic threefold to the enriched Euler number. When k = R this geometric interpretation agrees with the Segre type defined by Finashin and Kharlamov.

• Monday, March 16, 2020, 3:15pm, Physics 119, Geometry/topology Seminar
TBA
Kyle Hayden (Columbia University, Mathematics)

• Tuesday, March 17, 2020, 1:00pm, Physics 235, Other Meetings And Events Seminar
Doctoral Preliminary Exam
Stephen McKean

• Tuesday, March 17, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Xiangxiong Zhang (Purdue)

• Wednesday, March 18, 2020, 12:00pm, Gross Hall 111, Thesis Defenses Seminar
"Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms"
Thomas Huong Tran

• Wednesday, March 18, 2020, 1:00pm, 113 Physics, Thesis Defenses Seminar
"Homeostasis-Bifurcation Singularities and Indentifiability of Feedforward Networks"
William Duncan

• Wednesday, March 18, 2020, 3:15pm, Physics 119, Number Theory Seminar
TBD
Margaret Bilu (Courant Institute of Mathematical Sciences (NYU), Mathematics)

TBD

• Thursday, March 19, 2020, 3:15pm, 119 Physics, Probability Seminar
TBA
Ted Cox (Syracuse, math)

• Friday, March 20, 2020, 11:45am, Gross Hall 103, Data Dialogue
Julia Lane and Ben Feder
Julia Lane and Ben Feder

LUNCH: 11:45 am SEMINAR: Noon

• Friday, March 20, 2020, 12:00pm, 130 Physics, CTMS Adventures in Theory Lecture
TBA
Weinan E (Princeton University)

• Friday, March 20, 2020, 3:15pm, Physics 119, Department of Mathematics Seminar
TBA
Emily Witt (Kansas University)

• Monday, March 23, 2020, 3:15pm, Physics 119, Triangle Topology Seminar
TBA
Yu Pan (MIT, Mathematics)

TBA

• Tuesday, March 24, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Daryl Deford (MIT, CSAIL)

• Wednesday, March 25, 2020, 12:00pm, Gross 330, Applied Math And Analysis Seminar
TBA
Wotao Yin (UCLA)

• Thursday, March 26, 2020, 3:15pm, Physics 119, Probability Seminar
Stochastic persistence and extinction
Alex Hening (Tufts)

A key question in population biology is understanding the conditions under which the species of an ecosystem persist or go extinct. Theoretical and empirical studies have shown that persistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we look at the competitive exclusion principle from ecology, which says in its simplest form that two species competing for one resource cannot coexist, and show how the random switching can facilitate coexistence.

• Thursday, March 26, 2020, 4:15pm, Physics 119, Thesis Defenses Seminar
Do Tran
Do Tran

• Thursday, March 26, 2020, 4:30pm, Gross Hall 359, Thesis Defenses Seminar
"A Geometric Approach to Biomedical Time Series Analysis"
John Malik

• Friday, March 27, 2020, 12:00pm, Gross Hall 324, Thesis Defenses Seminar
"Minimal Resolutions of Monomial Ideals"
Erika Ordog

• Friday, March 27, 2020, 1:30pm, Physics 119, Mathematical Biology Seminar
Microbial community dynamics in time and space
Lingchong You (Duke University, Biomedical Engineering)

Microbes are by far the most dominant forms of life on earth. In every imaginable habitat, they form complex communities that carry out diverse functions. Microbial communities drive the geochemical cycling of diverse chemicals and through these activities shape the earth’s climate and environment. They are also intimately tied to human physiology and health. Members of each microbial community may compete for resources, collaborate to process the resources or to cope with stress. They communicate with each other by producing and responding to signaling molecules. They innovate by exchanging genetic materials. These interactions raise fundamental questions regarding the evolutionary and ecological forces that shape microbial consortia. Our lab has adopted a combination of quantitative biology and synthetic biology to explore these questions, often guided by mathematical modeling. We engineer gene circuits to program dynamics of one or more bacterial populations and use them to examine questions in cellular signal processing, evolution, ecology, and development. Analysis of these systems has provided insights into bacterial tolerance to antibiotics, developmental pattern formation, and scaling, as well as strategies to use bacteria to living fabricate functional materials by exploiting programmed self-organization. I will discuss our recent efforts in analyzing microbial community dynamics mediated by gene transfer.

• Saturday, March 28, 2020, 9:00am, Fitzpatrick Center Schiciano Auditorium, Machine Learning Day
Machine Learning Day
Keynote: Katherine Gorman

Keynote:10-10:45am Registration and Breakfast 10:45am - 11am: Intro to Event 11-11:45am: Keynote Speaker (Kat Gorman, Title: The Littlest Robot Is The One You Should Fear The Most: Thinking about the public conversation on AI and how you can make it more realistic ) 11:45-12pm Break 12-1pm Research spotlight presentations Olivier Binette: Assessing the Accuracy of Slavery Prevalence Estimates 1-2pm Lunch and poster presentations 2-2:45pm Panel Discussion with BOW 2-2:45pm Carmel Lee: Grant Writing for Beginners 2:45-3pm Break 3-3:45pm Valassis Talk 3-3:45pm Kyle Bradbury: Machine Learning in Under 1 Hour 3:45-4pm Break 4-4:45 Josh Jelin: Preparing for Industry ~4:45pm End of ML day

• Monday, March 30, 2020, 12:00pm, 119 Physics, Graduate/faculty Seminar
Pictures of supersymmetry and its friends
Kevin Iga (Pepperdine University)

Supersymmetry is a promising idea in particle physics that posits a relationship between the two kinds of particles in nature: bosons and fermions. In 2004, two physicists, M. Faux and S.J. Gates, have developed a new approach to the subject. This approach involves certain decorated graphs called Adinkras, which are a visual and accessible way to understand supersymmetry. In the years since then, the study of Adinkras has, in turn, drawn on surprising connections with other areas of math, like error correcting codes, algebraic topology, combinatorics, and Riemann surfaces. Conversely, Adinkras provide a possible avenue for making many of these topics more accessible.

• Monday, March 30, 2020, 1:00pm, MSRB1 #001 Seminar Room, Thesis Defenses Seminar
Sex-specific Computational Models of Blood Pressure Regulation
Jessica Leete

• Monday, March 30, 2020, 1:00pm, Physics 235, Thesis Defenses Seminar
"Analytical and Numerical Study of Lindblad Equations"
Yu Cao

• Monday, March 30, 2020, 3:15pm, Physics 119, Geometry/topology Seminar
Singular fibres of (holomorphic) Lagrangian fibrations
Justin Sawon (UNC Chapel Hill, Mathematics)

Compact holomorphic Lagrangian fibrations are higher-dimensional analogues of elliptic K3 surfaces. Their generic fibres are abelian varieties and singular fibres occur in complex codimension one. The structure of singular fibres in codimension one was studied by Matsushita (using toric degeneration) and by Hwang-Oguiso (using complex analytic techniques). A great deal more is known for elliptic K3 surfaces, and in this talk we consider what can be generalized to higher-dimensions.

• Tuesday, March 31, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Pedro Aceves Sanchez (NC State)

• Wednesday, April 1, 2020, 12:00pm, 119 Physics, Applied Math And Analysis Seminar
Vortex stretching and a modified zeroth law for the incompressible 3D Navier-Stokes equations
Tsuyoshi Yoneda (The University of Tokyo)

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the incompressible 3D Navier-Stokes equations. More precisely, we consider the NS equations under the following $2+\frac{1}{2}$-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove a modified version of the zeroth law (but very close to the actual zeroth-law) induced by such vortex-stretching. This is a joint work with In-Jee Jeong.

• Thursday, April 2, 2020, 3:15pm, 119 Physics, Probability Seminar
TBA
Avanti Athreya (Johns Hopkins)

• Friday, April 3, 2020, 11:45am, Gross Hall 103, Data Dialogue
Barak Sober (Duke)
Barak Sober

My research ranges between analysis of high dimensional data from a geometrical perspective and the application of mathematical and statistical methods in digital humanities (in the context of Archaeology and Art History).

• Friday, April 3, 2020, 12:00pm, Physics 119, Mathematical Biology Seminar
TBA
Jacob Scott (Cleveland Clinic)

• Friday, April 3, 2020, 3:15pm, Physics 119, Algebraic Geometry Seminar
A refined Brill-Noether theory over Hurwitz spaces
Hannah Larson (Stanford University, Mathematics)

The celebrated Brill-Noether theorem says that the space of degree d maps of a general genus g curve to P^r is irreducible. However, for special curves, this need not be the case. Indeed, for general k-gonal curves (degree k covers of P^1), this space of maps can have many components, of different dimensions (Coppens-Martens, Pflueger, Jensen-Ranganathan). In this talk, I will introduce a natural refinement of Brill-Noether loci for curves with a distinguished map C -> P^1, using the splitting type of push forwards of line bundles to P^1. In particular, studying this refinement determines the dimensions of all irreducible components of Brill-Noether loci of general k-gonal curves.

• Monday, April 6, 2020, 12:00pm, Physics 119, Graduate/faculty Seminar
TBD
Chao Shen (Duke University)

TBD

• Monday, April 6, 2020, 3:15pm, Physics 119, Geometry/topology Seminar
TBA
John Lind (CSU-Chico)

• Wednesday, April 8, 2020, 3:15pm, Physics 119, Number Theory Seminar
The Semiring of Formal Differences
Keith Pardue

For rings, there is a natural bijection between (two-sided) ideals and congruences, but for semirings (where we do not require additive inverses), this correspondence breaks. Many basic notions concerning ideals in rings thus split into two different notions for semirings, one for ideals and the other for congruences. Currently there is interest in extensions of scheme theory to commutative semirings, motivated especially by ideas concerning the "field of one element" in arithmetic geometry. To do so, we must decide if we would rather talk about prime ideals or about prime congruences; if the latter then we must decide what we mean by a prime congruence. Of the several definitions of a prime congruence put forward, the most promising is due to Joó and Mincheva. In this talk, we will see that the congruences in a semiring $$R$$ are themselves special ideals in a different semiring $$R_{fd}$$, the semiring of formal differences for $$R$$. Then Joó and Mincheva's prime congruences are precisely those congruences that are prime ideals in $$R_{fd}$$. We will also examine Joó and Mincheva's natural arithmetic of congruences in comparison with classical arithmetic of ideals. The natural numbers $$\mathbb{N}$$ is already a rich example for this story. We will end with an alternative multiplication law for congruences on $$\mathbb{N}$$ that better extends the arithmetic of ideals in $$\mathbb{Z}$$ than Joó and Mincheva's. In particular, this alternative multiplication law distributes over sum of congruences and admits unique factorization of congruences into prime congruences.

• Wednesday, April 8, 2020, 3:30pm, Gross Hall, Ahmadieh Family Grand Hall, Room 330, Machine Learning Seminar

RECEPTION: 3:00 p.m. SEMINAR: 3:30 p.m.

• Thursday, April 9, 2020, 3:15pm, 119 Physics, Probability Seminar
TBA
Allan Sly (Princeton, Mathematics)

• Friday, April 10, 2020, 12:00pm, TBA, Colloquium Seminar
TBA
Allan Sly (Princeton University)

• Monday, April 13, 2020, 12:00pm, Physics 119, Graduate/faculty Seminar
TBD
Didong Li (Duke University)

• Tuesday, April 14, 2020, 4:30pm, Physics 128, Public Lectures Seminar
PLUM: TBA

TBA

• Wednesday, April 15, 2020, 12:00pm, Physics 119, Number Theory Seminar
TBA

TBA

• Wednesday, April 15, 2020, 12:00pm, TBA, Colloquium
An improvement of Liouville’s theorem for discrete harmonic functions
Eugenia Malinnikova (Stanford University)

The classical Liouville theorem tells us that a bounded harmonic function on the plane is a constant. At the same time for any (arbitrarily small) angle on the plane there exist non-constant harmonic functions that are bounded everywhere outside this angle. The situation is completely different for discrete harmonic functions on the standard square lattices. The following strong version of the Liouville theorem holds on the two-dimensional lattice. If a discrete harmonic function is bounded on 99% of the lattice then it is constant. A simple counter-example shows that in higher dimensions such improvement is no longer true.

The talk is based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.

• Wednesday, April 15, 2020, 3:15pm, Physics 119, Number Theory Seminar
TBA
Lennart Gehrmann (University of Duisburg-Essen/McGill University)

• Friday, April 17, 2020, 12:00pm, 119 Physics, Mathematical Biology Seminar
TBA
Heiko Enderling (Moffitt cancer center)

• Monday, April 20, 2020, 3:15pm, 119 Physics, Geometry/topology Seminar
TBA
Ao Sun (Massachusetts Institute of Technology)

TBA

• Tuesday, April 21, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
Prediction of random and chaotic dynamics in nonlinear optics
Amir Sagiv (Columbia)

The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the nonlinear Schrodinger equation (NLS) model of laser propagation, beams lose their initial phase information in the presence of input noise. Thus, the interactions between beams become unpredictable as well. Not all is lost, however. The statistics of many interactions are predictable by a universal model. Computationally, the universal model is efficiently solved using a novel spline-based stochastic computational method. Our algorithm efficiently estimates probability density functions (PDF) that result from differential equations with random input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results and analysis at the intersection of probability and approximation theory.

• Wednesday, April 22, 2020, 3:15pm, 119 Physics, Number Theory Seminar
TBA
Wei Zhang (MIT)

• Tuesday, April 28, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Jongchon Kim (UBC)

• Tuesday, May 12, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Xiaoping Wang (USTHK)

• Wednesday, September 9, 2020, 12:00pm, Physics 119, Frontiers In Mathematics Distinguished Lecture Series
Lecture 1 (Frontiers in Mathematics)
Hong Wang (IAS)

(This is the first talk in the Frontiers in Mathematics Distinguished Lecture Series. See also the second talk in the series, on Friday September 11 at noon.)

• Friday, September 11, 2020, 12:00pm, Physics 119, Frontiers In Mathematics Seminar (second of 2 lectures)
Lecture 2 (Frontiers in Mathematics)
Hong Wang (IAS)

(This is the second talk in the Frontiers in Mathematics Distinguished Lecture Series. See also the first talk on Wednesday September 9 at noon.)

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