2018 Jan 09

# Dynamics Lunch: Raimundo Briceno (TAU) "A Breiman type theorem for Gibbs measures"

12:00pm to 1:00pm

We will review a Breiman type theorem for Gibbs measures due to Gurevich and Tempelman. For a translation invariant Gibbs measure on a suitable translation invariant configuration set X \subset S^G, where G is an amenable group and S is a finite set, we will prove the convergence of the Shannon-McMillan-Breiman ratio on a specific subset of "generic" configurations. Provided that the above Gibbs measure exists, we also prove the convergence in the definition of pressure and the fact that this Gibbs measure is an equilibrium state.
2017 Apr 27

# Basic notions: Raz Kupferman

4:00pm to 5:15pm

Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
2018 Jan 04

# Basic Notions Seminar: Zlil Sela (HUJI) - "Projection complexes, actions on quasi-trees, and applications to mapping class groups of surfaces" (after Bestvina-Bromberg-Fujiwara).

4:00pm to 5:15pm

## Location:

Ross 70
Projection complexes, actions on quasi-trees, and applications to mapping class groups of surfaces (after Bestvina-Bromberg-Fujiwara).
2017 Mar 02

# Basic Notions: Ori Gurel Gurevich (HUJI) - On Smirnov's proof of conformal invariance of critical percolation

4:00pm to 5:00pm

## Location:

Manchester Building, Lecture Hall 2
Abstract:

Let G be an infinite connected graph. For each vertex of G we decide
randomly and independently: with probability p we paint it blue and
with probability 1-p we paint it yellow. Now, consider the subgraph of
blue vertices: does it contain an infinite connected component?

There is a critical probability p_c(G), such that if p>p_c then almost
surely there is a blue infinite connected component and if pp_c or p<p_c.

We will focus on planar graphs, specifically on the triangular
2018 Jan 11

# Basic Notions: Michael Hopkins (Harvard) - Homotopy theory and algebraic vector bundles

4:00pm to 5:15pm

## Location:

Einstein 2
Abstract: This talk will describe joint work with Aravind Asok and Jean Fasel using the methods of homotopy theory to construct new examples of algebraic vector bundles. I will describe a natural conjecture which, if true, implies that over the complex numbers the classification of algebraic vector bundles over smooth affine varieties admitting an algebraic cell decomposition coincides with the classification of topological complex vector bundles.
2018 Jan 14

# Kazhdan Sunday seminars: Tomer Schlank (HUJI) "Topics in algebraic topology".

11:00am to 1:00pm

## Location:

Ross buildings, Room 70A.
10:00-11:00 We will have a special lecture on string diagrams by Shaul Barkan 11:00-13:00 Asaf Horev will continue his talk about ambidexterity and duality
2018 Jan 14

# Kazhdan Sunday seminars: Leonid Polterovich (TAU) "Algebraic methods in symplectic topology"

3:00pm to 5:00pm

## Location:

Ross buildings, Room 70A.
Nick Rozenblyum (Chicago) will talk about Tamarkin's category.
2017 Dec 27

# Jerusalem Analysis Seminar: "Optimal Gaussian Partitions", Elchanan Mossel (MIT)

12:00pm to 1:00pm

## Location:

Ross 70

How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution. The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in the context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

2016 Nov 22

# SPECIAL Analysis and PDEs seminar -D. Fajman "Dynamics of Spacetime — Einstein’s equations as a geometric flow."

11:00am to 12:00pm

Ross 70
Abstract:
2017 Apr 27

# PDE and Analysis Seminar: Grzegorz Swiderski (Wroclaw)

1:00pm to 2:00pm

## Location:

Ross 70
Title: Asymptotics of Christoffel functions in an unbounded setting Abstract: Consider a measure $\mu$ supported on the real line with all moments finite. Let $(p_n : n \geq 0)$ be the corresponding sequence of orthonormal polynomials. This sequence satisfies the three-term recurrence relation $a_{n-1} p_{n-1}(x) + b_n p_n(x) a_n p_{n+1}(x) = x p_n(x) \quad (n > 0)$ for some sequences $a$ and $b$. One defines the $n$th Christoffel function by $\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.$ In the talk, under some regularity hypotheses on $a$ and $b$, we show
2017 Dec 06

# Jerusalem Analysis and PDEs seminar: "Asymptotics of the ground state energy for relativistic heavy atoms and molecules" Victor Ivrii (Toronto)

12:00pm to 1:00pm

## Location:

Ross 70.
We discuss sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, without magnetic field or with the self-generated magnetic field, and, in particular, relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. In particular, we conclude that the Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.
2016 Nov 10

# Analysis and PDEs - Maurice Duits (KTH) Title: Global fluctuations for non-colliding processes

1:00pm to 2:00pm

## Location:

Ross 70
In this talk we will discuss the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. By viewing the paths as level lines these systems give rise to random (stepped) surfaces. When the number of paths is large a limit shape appears. The fluctuations for the random surfaces are believed to be universally described by the Gaussian Free Field.
2017 Nov 22

# Jerusalem Analysis Seminar: "Inverse Problems with applications to Cryo-Electron Microscopy (cryo-EM)",Roy Lederman

12:00pm to 1:00pm

## Location:

Ross 70
Abstract: Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
2017 Mar 16

# Analysis and PDEs: Mayukh Mukherjee (Technion) - Some asymptotic estimates on the geometry of Laplace eigenfunctions

1:00pm to 2:00pm

## Location:

Ross 70
Given a closed smooth Riemannian manifold M, the Laplace operator is known to possess a discrete spectrum of eigenvalues going to infinity. We are interested in the properties of the nodal sets and nodal domains of corresponding eigenfunctions in the high energy limit. We focus on some recent results on the size of nodal domains and tubular neighbourhoods of nodal sets of such high energy eigenfunctions (joint work with Bogdan Georgiev).