2018
Dec
11

# Events & Seminars

2019
Jan
09

2018
Dec
26

# Analysis Seminar: Rachel Greenfeld (BIU)

12:00pm to 1:00pm

## Location:

Room 70, Ross Building

Title: Fuglede's spectral set conjecture for convex polytopes.

Abstract:

A set \Omega \subset \mathbb{R}^d is called spectral if the space L^2(\Omega) admits an orthogonal basis of exponential functions. Back in 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. This conjecture inspired extensive research over the years, but nevertheless, the precise connection between the notions of spectrality and tiling, is still a mystery.

Abstract:

A set \Omega \subset \mathbb{R}^d is called spectral if the space L^2(\Omega) admits an orthogonal basis of exponential functions. Back in 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. This conjecture inspired extensive research over the years, but nevertheless, the precise connection between the notions of spectrality and tiling, is still a mystery.

2018
Nov
07

# Analysis Seminar: Elik Olami (HUJI) "Homogenization of edge dislocations via de-Rham currents"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building

Title: Homogenization of edge dislocations via de-Rham currents

2018
Nov
06

2018
Dec
12

# Analysis Seminar: Barry Simon "Poncelet’s Theorem, Paraorthogonal Polynomials and the Numerical Range of Truncated GGT matrices"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building

Abstract: During the last 20 years there has been a considerable literature on a collection of related mathematical topics: higher degree versions of Poncelet’s Theorem, certain measures associated to some finite Blaschke products and the numerical range of finite dimensional completely non-unitary contractions with defect index 1. I will explain that without realizing it, the authors of these works were discussing OPUC.

2018
Nov
28

# Analysis Seminar: Netanel Levi "A decomposition of the Laplacian on symmetric metric graphs"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building

Title: A decomposition of the Laplacian on symmetric metric graphs

Abstract

The spectrum of the Laplacian on graphs which have certain symmetry properties can be studied via a decomposition of the operator as a direct sum of one-dimensional operators which are simpler to analyze. In the case of metric graphs, such a decomposition was described by M. Solomyak and K. Naimark when the graphs are radial trees. In the discrete case, there is a result by J. Breuer and M. Keller treating more general graphs.

Abstract

The spectrum of the Laplacian on graphs which have certain symmetry properties can be studied via a decomposition of the operator as a direct sum of one-dimensional operators which are simpler to analyze. In the case of metric graphs, such a decomposition was described by M. Solomyak and K. Naimark when the graphs are radial trees. In the discrete case, there is a result by J. Breuer and M. Keller treating more general graphs.

2018
Dec
31

# NT&AG: Eyal Subag (Penn State University), "Symmetries of the hydrogen atom and algebraic families"

2:30pm to 3:30pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel

The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.

2018
Nov
21

# Analysis Seminar: Asaf Shachar (HUJI) "Regularity via minors and applications to conformal maps"

12:00pm to 1:00pm

## Location:

Room 70, Ross Building

Title:

Regularity via minors and applications to conformal maps.

Abstract:

Let f:\mathbb{R}^n \to \mathbb{R}^n be a Sobolev map; Suppose that the k-minors of df are smooth. What can we say about the regularity of f?

This question arises naturally in the context of Liouville's theorem, which states that every weakly conformal map is smooth. I will explain the connection of the minors question to the conformal regularity problem, and describe a regularity result for maps with regular minors.

Regularity via minors and applications to conformal maps.

Abstract:

Let f:\mathbb{R}^n \to \mathbb{R}^n be a Sobolev map; Suppose that the k-minors of df are smooth. What can we say about the regularity of f?

This question arises naturally in the context of Liouville's theorem, which states that every weakly conformal map is smooth. I will explain the connection of the minors question to the conformal regularity problem, and describe a regularity result for maps with regular minors.

2018
Oct
18

# Colloquium: Rahul Pandharipande (ETH Zürich) - Zabrodsky Lecture: Geometry of the moduli space of curves

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. The talk is about the search for a cohomology calculus for the moduli space of curves parallel to what is known for better understood geometries.

2018
Dec
06

# Colloquium: Naomi Feldheim (Bar-Ilan) - A spectral perspective on stationary signals

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

A ``random stationary signal'', more formally known as a Gaussian stationary function, is a random function f:R-->R whose distribution is invariant under real shifts (hence stationary), and whose evaluation at any finite number of points is a centered Gaussian random vector (hence Gaussian).

The mathematical study of these random functions goes back at least 75 years, with pioneering works by Kac, Rice and Wiener, who were motivated both by applications in engineering and

by analytic questions about ``typical'' behavior in certain classes of functions.

The mathematical study of these random functions goes back at least 75 years, with pioneering works by Kac, Rice and Wiener, who were motivated both by applications in engineering and

by analytic questions about ``typical'' behavior in certain classes of functions.

2019
Jun
27

# Colloquium Dvoretzky lecture: Assaf Naor(Princeton) - An average John theorem

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

__Abstract__: We will prove a sharp average-case variant of a classical embedding theorem of John through the theory of nonlinear spectral gaps. We will use this theorem to provide a new answer to questions of Johnson and Lindenstrauss (1983) and Bourgain (1985) on metric dimension reduction, and explain how it leads to algorithms for approximate nearest neighbor search.

2019
Jan
03

# Colloquium: Nati Linial (HUJI) - Graph metrics

2:30pm to 3:30pm

A finite graph is automatically also a metric space, but is there any interesting geometry to speak of? In this lecture I will try to convey the idea that indeed there is very interesting geometry to explore here. I will say something on the local side of this as well as on the global aspects. The k-local profile of a big graph G is the following distribution. You sample uniformly at random k vertices in G and observe the subgraph that they span. Question - which distributions can occur? We know some of the answer but by and large it is very open.

2019
Apr
18

# Passover

(All day)

2018
Oct
25

# Colloquium: Karim Adiprasito (HUJI) - Combinatorics, topology and the standard conjectures beyond positivity

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2 or higher can it have? How dense can they be?

This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar).

All notions used will be explained in the talk (I will make an effort to be very elementary)

This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar).

All notions used will be explained in the talk (I will make an effort to be very elementary)