- Wednesday, October 17, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*Deep Learning-Based Numerical Methods for High-Dimensional Parabolic PDEs and Forward-Backward SDEs*

Jiequn Han (Princeton University)- Developing algorithms for solving high-dimensional partial differential equations (PDEs) and forward-backward stochastic differential equations (FBSDEs) has been an exceedingly difficult task for a long time, due to the notorious difficulty known as the curse of dimensionality. In this talk we introduce a new type of algorithms, called "deep BSDE method", to solve general high-dimensional parabolic PDEs and FBSDEs. Starting from the BSDE formulation, we approximate the unknown Z-component by neural networks and design a least-squares objective function for parameter optimization. Numerical results of a variety of examples demonstrate that the proposed algorithm is quite effective in high-dimensions, in terms of both accuracy and speed. We furthermore provide a theoretical error analysis to illustrate the validity and property of the designed objective function.

- Thursday, October 18, 2018, 3:15pm, 119 Physics, Probability Seminar
*Extreme Level Sets of Branching Brownian Motion*

Lisa Hartung (Courant Institute)- Branching Brownian motion is a classical process in probability theory belonging to the class of “Log-correlated random fields”. We study the structure of extreme level sets of this process, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height and shape of those clusters which carry such level sets. We also find the right tail decay of the distribution of the distance between the two highest particles. These results confirm two conjectures of Brunet and Derrida.(joint work with A. Cortines, O Louidor)

- Thursday, October 18, 2018, 3:30pm, 298 Physics (Physics Faculty Lounge), String Theory Seminar
*Graded Quivers, Toric Calabi Yaus and B-Branes*

Azeem Hasan- Recently introduced m-graded quivers provide a unified language for describing gauge theories with minimal amount of supersymmetry and their dualities in various dimensions. The prototypical example of these are gauge theories on D-branes probing Calabi-Yau singularities. In this talk after reviewing how m-graded quivers encode various constraints on these theories, I will describe some general methods of constructing these quivers and use them to construct a few infinite families of them. Lastly I will explain how these quivers describe Topological B-model on toric Calabi-Yaus.

- Friday, October 19, 2018, 3:15pm, 119 Physics, Number Theory Seminar
*Relative trace formula of Jacquet-Rallis, recent progress*

Michal Zydor (University of Michigan, Mathematics)- I will discuss the relative trace formula approach to the global Gan-Gross-Prasad conjectures for unitary groups. The focus will be on the spectral side. I will present the various terms that appear in the spectral development of the relative trace formula and discuss what is still missing. This is a joint work with Pierre-Henri Chaudouard.

- Monday, October 22, 2018, 3:15pm, 119 Physics, Triangle Topology Seminar
*TBA*

Thomas Mark (University of Virginia, Mathematics) - Wednesday, October 24, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Almut Burchard (U of Toronto) - Friday, October 26, 2018, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*TBA*

Remy van Dobben de Bruyn (Institue for Advanced Study)- Abstract: In the sixties, Serre constructed a smooth projective variety in characteristic p that cannot be lifted to characteristic 0. If a variety does not lift, a natural question is whether some variety related to it does. We construct a smooth projective variety that cannot be rationally dominated by a smooth projective variety that lifts.

- Monday, October 29, 2018, 12:00pm, TBA, Applied Math And Analysis Seminar
*TBA*

Anna Mazzucato (Pennsylvania State University) - Monday, October 29, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
*Hyperbolic structures on wreath products*

Sahana Balasubramanya (UNC Greensboro)- The poset of hyperbolic structures on a group G is still very far from being understood and several questions remain unanswered. In this talk, I will speak about some new results that describe hyperbolic structures on the wreath product Gwr Z, for any group G. As a consequence, I answer two open questions regarding quasi-parabolic structures: I will give an example of a group G with an uncountable chain of quasi-parabolic structures and give examples of groups that have finitely many quasi-parabolic structures.

- Tuesday, October 30, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
*Augmentations and sheaves for knot conormals*

Honghao Gao (Institut Fourier)- Knot invariants can be defined using Legendrian isotopy invariants of the knot conormal. There are two types of invariants raised in this way: one is the knot contact differential graded algebra together with augmentations associated to this dga, and the other one is the category of simple sheaves microsupported along the knot conormal. The Nadler-Zaslow correspondence suggests a connection between the two types of invariants. In this talk, I will manifest an explicit map between augmentations and simple sheaves.

- Wednesday, October 31, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Guillaume Bal (University of Chicago) - Wednesday, October 31, 2018, 3:15pm, 119 Physics, Number Theory Seminar
*TBD*

Jessica Fintzen (Michigan/Cambridge) - Thursday, November 1, 2018, 3:15pm, 119 Physics, Probability Seminar
*The Contact Process on random graphs and Galton-Waton trees*

Rick Durrett- Practice talk for Northeast Probability Symposium. This is joint work with Zoe Huang. We will also mention two results from the DOMath summer project.

- Thursday, November 1, 2018, 3:30pm, 298 Physics (Physics Faculty Lounge), String Theory Seminar
*TBA*

Laura Donnay - Friday, November 2, 2018, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*TBA*

Wei Ho- TBA

- Monday, November 5, 2018, 12:00pm, 119 Physics, Graduate/faculty Seminar
*Locally Linear Embedding and Dirichlet Boundary*

Nan Wu - Monday, November 5, 2018, 3:15pm, 119 Physics, Triangle Topology Seminar
*TBA*

Hannah Schwartz (Bryn Mawr College, Mathematics) - Monday, November 5, 2018, 4:30pm, 330 Gross Hall, Ahmadieh Family Grand Hall, Undergraduate Seminar Talk Seminar
*Machine Learning for Population Health and Disease Surveillance*

Daniel B. Neill (New York University, Mathematics Department)- Over the past decade, we have developed a variety of new machine learning approaches for early and accurate detection of emerging outbreaks of disease. This talk will describe our work in addressing three distinct public health challenges: syndromic surveillance using small-area count data, drug overdose surveillance using multidimensional case data, and pre-syndromic surveillance using free-text emergency department chief complaints. In the first problem setting, we monitor a set of known syndrome types (e.g., gastrointestinal illness) and identify space-time clusters of disease. In the second problem setting, we use the multiple dimensions of each case (age, race, gender, location, and drug types) to identify emerging patterns of fatal accidental overdoses affecting specific subpopulations. In the third problem setting, we identify clusters of cases that are of interest to public health but do not correspond to existing syndrome categories, such as “novel” disease outbreaks with previously unseen patterns of symptoms. Across all three problem settings, we develop new “fast subset scan” approaches to deal with the size and complexity of real-world data. Subset scanning is a novel pattern detection approach which treats the detection problem as a search over subsets of data records and attribute values, finding those subsets which maximize an expectation-based scan statistic. One key insight is that this search over subsets can be performed very efficiently, reducing run times from years to milliseconds, using the "linear-time subset scanning" property of many commonly used likelihood ratio scan statistics. These fast subset scanning approaches enable accurate, precise, and computationally efficient detection of emerging public health threats, providing state and local health departments with the situational awareness needed for early and targeted interventions.

- Wednesday, November 7, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Weijie Su (University of Pennsylvania) - Thursday, November 8, 2018, 3:15pm, 119 Physics, Probability Seminar
*title*

Pascal Maillard (CRM (Montréal) and Université Paris-Sud)- abstract

- Thursday, November 8, 2018, 3:30pm, 298 Physics (Physics Faculty Lounge), String Theory Seminar
*TBA*

Prahar Mitra - Friday, November 9, 2018, 12:00pm, TBA, Applied Math And Analysis Seminar
*Non-Equilibrium Steady States for Networks of Oscillators*

Noé Cuneo (Université Paris VI, Mathematics)- Non-equilibrium steady states for chains of oscillators interacting with stochastic heat baths at different temperatures have been the subject of several studies. In this talk I will discuss how to generalize these results to multidimensional networks of oscillators. I will first introduce the model and motivate it from a physical point of view. Then, I will present conditions on the topology of the network and on the interaction potentials which imply the existence and uniqueness of the non-equilibrium steady state, as well as exponential convergence to it. The two main ingredients of the proof are (1) a controllability argument using Hörmander's bracket criterion and (2) a careful study of the high-energy dynamics which leads to a Lyapunov-type condition. I will also mention cases where the non-equilibrium steady state is not unique, and cases where its existence is an open problem. This is joint work with J.-P. Eckmann, M. Hairer and L. Rey-Bellet, Electronic Journal of Probability 23(55): 1-28, 2018 (arXiv:1712.09413).

- Friday, November 9, 2018, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*TBA*

Benjamin Bakker (University of Georgia)- TBA

- Monday, November 12, 2018, 12:00pm, 119 Physics, Graduate/faculty Seminar
*TBA*

Aaron Pollack - Monday, November 12, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

David Duncan (James Madison University, Mathematics)- TBA

- Wednesday, November 14, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*Finite Difference Methods for Boundary Value Problems: Using Interface Problems*

Tom Beale (Duke University)- Finite difference methods are awkward for solving boundary value problems, such as the Dirichlet problem, with general boundaries, but they are well suited for interface problems, which have prescribed jumps in an unknown across a general interface or boundary. The two problems can be connected through potential theory: The Dirichlet boundary value problem is converted to an integral equation on the boundary, and the integrals can be thought of as solutions to interface problems. Wenjun Ying et al. have developed a practical method for solving the Dirichlet problem, and more general ones, by solving interface problems with finite difference methods and iterating to mimic the solution of the integral equation. We will describe some analysis which proves that a simplified version of Ying's method works. A recent view of classical potential theory leads to a finite difference version of the theory in which, remarkably, the crude discrete operators have much of the structure of the exact operators. This simplified method produces the Shortley-Weller solution of the Dirichlet problem. Details can be found at arxiv.org/abs/1803.08532 .

- Friday, November 16, 2018, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*TBA*

Julie Rana- TBA

- Monday, November 19, 2018, 12:00pm, 119 Physics, Graduate/faculty Seminar
*TBA*

Erin Beckman - Monday, November 19, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Ina Petkova (Dartmouth College, Mathematics) - Monday, November 26, 2018, 12:00pm, 119 Physics, Graduate/faculty Seminar
*TBA*

Siming He - Monday, November 26, 2018, 3:15pm, 119 Physics, Triangle Topology Seminar
*TBA*

Lisa Piccirillo (University of Texas, Austin, Mathematics) - Wednesday, November 28, 2018, 3:15pm, 119 Physics, Number Theory Seminar
*TBA*

June Huh (IAS and Princeton) - Friday, November 30, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Elina Robeva (MIT) - Monday, December 3, 2018, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Curtis Porter (NCSU, Mathematics)- TBA

- Monday, December 3, 2018, 4:30pm, TBA, Public Lectures Seminar
*PLUM: TBA*

Rachel Levy (MAA) - Thursday, December 6, 2018, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Kevin McGoff - Friday, February 8, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*TBA*

Yiannis Sakellaridis (Rutgers University-Newark) - Friday, February 22, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
- tentative: Sebastian Casalaina-Martin

- Friday, March 22, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
- tentative: Sebastian Casalaina-Martin

- Wednesday, March 27, 2019, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Alina Chertock (NC State) - Thursday, March 28, 2019, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Kavita Ramanan (Brown) - Friday, April 5, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
- tentative: Sebastian Casalaina-Martin

- Wednesday, April 24, 2019, 12:00pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Stefan Steinerberger (Yale University)

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