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.

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2018
Jan
14

3:00pm to 5:00pm

Ross buildings, Room 70A.

Nick Rozenblyum (Chicago) will talk about Tamarkin's category.

2017
Dec
27

12:00pm to 1:00pm

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. Read more about Jerusalem Analysis Seminar: "Optimal Gaussian Partitions", Elchanan Mossel (MIT)

2016
Nov
22

2017
Apr
27

1:00pm to 2:00pm

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

12:00pm to 1:00pm

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

1:00pm to 2:00pm

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

12:00pm to 1:00pm

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

1:00pm to 2:00pm

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).

2017
Jun
15

1:00pm to 2:00pm

Ross 70

Title: Quantum state transfer on graphs.
Abstract:
Transmitting quantum information losslessly through a network of particles is an important problem in quantum computing. Mathematically this amounts to studying solutions of the discrete Schrödinger equation d/dt phi = i H phi, where H is typically the adjacency or Laplace matrix of the graph. This in turn leads to questions about subtle number-theoretic behavior of the eigenvalues of H.

2016
Jul
30

10:00am to 11:00am

2017
Nov
15

12:00pm to 1:00pm

Ross 70 (NOTE LOCATION!)

Abstract: We will discuss the question: for a random walk in a random environment, when should one expect a central limit theorem, i.e. that after appropriate scaling, the random walk converges to Brownian motion? The answer will turn out to involve the spectral theory of unbounded operators. All notions will be defined in the talk. Joint work with Balint Toth.

2017
Mar
09

12:00pm to 1:00pm

Ross 70

I will present an overview of some recent progress on the study of the nodal sets of Steklov eigenfunctions. In particular, I will discuss sharp estimates on the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary obtained in my joint
work with D. Sher and J. Toth.

2017
May
18

1:00pm to 2:00pm

Ross 70

Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.

2016
Mar
31

1:00pm to 2:30pm

Ross 70

Title: No-gaps delocalization for general random matrices.
Abstract:

2017
Dec
20

12:00pm to 1:00pm

Ross 70

20 years ago Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions using tools from dynamical systems. In this talk, we will present another elementary construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such measures.