Eventss

2019 Dec 19

Basic Notions: Yoel Groman (HUJI) "Hamiltonian dynamics and classical mirror symmetry".

4:00pm to 5:15pm

Location: 

Ross 70
Physicists have observed in the '80s that Calabi-Yau manifolds come in pairs so that quantum cohomology on the one is related to period integrals on the other. This phenomenon, known as mirror symmetry, has since evolved into a deeper understanding that symplectic geometry on a manifold is typically encoded in the complex geometry of another, its mirror. I will discuss in some simple examples of how the relation arises naturally from the study of Hamiltonian Floer cohomology associated with invariant sets of an integrable system.
2019 Dec 09

NT Seminar - Eyal Kaplan

2:30pm to 3:30pm

Location: 

Ross 70

Title: The generalized doublingmethod and its applications
Abstract: The doubling method,first introduced by Piatetski-Shapiro and Rallis in the 80s, has had numerousapplications, e.g. to the theta correspondence and to arithmetic problems.In a series of recent works this method was generalized in severalaspects, with an application to functoriality from classical groups to GL(N).The most recent result is a multiplicityone theorem (joint work with Gourevitch and Aizenbud).
I will brieflysurvey the method and talk about some of its applications.
2019 Dec 24

Dor Elimelech (BGU) Restricted permutations and perfect matchings

2:30pm to 3:30pm

Abstract:
A restricted permutation of a locally finite directed graph $G=(V,E)$ is a vertex permutation $\pi: V\to V$ for which $(v,\pi(v))\in E$, for any vertex $v\in V$. The set of such permutations, denoted by $\Omega(G)$, with a group action induced from a subset of graph isomorphisms form a topological dynamical system. In the particular case presented by Schmidt and Strasser (2016), where $V=\mathbb{Z}^d$ and $(n,m)\in E$ iff $(n-m)\in A$ ($A\subseteq \mathbb{Z^d}$ is fixed), $\Omega(G)$ is a subshift of finite type.
2020 Jan 15

Analysis Seminar Dvoretsky Lecture: Sylvia Serfaty (NYU Courant) - Mean Field Limits for Coulomb Dynamics

12:00pm to 1:00pm

Location: 

Ross 70
We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation. This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity.
2019 Dec 17

Nishant Chandgotia (HUJI), Predictive sets.

2:00pm to 3:00pm

Location: 

Ross 70
Abstract: A subset of the integers P is called predictive if for all zero-entropy processes X_i; i in Z, X_0 can be determined by X_i; i in P. The classical formula for entropy shows that the set of natural numbers forms a predictive set. In joint work with Benjamin Weiss, we will explore some necessary and some sufficient conditions for a set to be predictive. These sets are related to Riesz sets (as defined by Y. Meyer) which arise in the study of singular measures. This and several questions will be discussed during the talk.
2020 Jan 16

Dvoretzky Lectures: Systems of points with Coulomb interactions

Lecturer: 

Sylvia Serfaty
2:30pm to 4:30pm

Location: 

Manchester House, Lecture Hall 2
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability.We will first review these motivations, then present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale.
2020 Jan 15

Dvoretzky Lectures: Mean Field Limits for Coulomb Dynamics

Lecturer: 

Sylvia Serfaty
12:00pm to 2:00pm

Location: 

Ross 70
We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation.  This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity.

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