2018 Nov 06

# Dynamics Lunch: Weikun He "Counterexamples to a conjecture of Woods, after Regev, Shapira and Weiss."

12:00pm to 1:00pm

## Location:

Manchester faculty club
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.
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 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.
2018 Oct 22

# Zabrodsky Lecture 3: CohFT calculations

## Lecturer:

Rahul Pandharipande (ETH Zurich)
2:00pm to 3:00pm

## Location:

Ross 70

I will explain how calculations of various natural classes on the moduli of curves fit into the CohFT framework. These include calculations related to Hilbert schemes of points, Verlinde bundles, and, if time permits, double ramification (DR) cycles.

2018 Oct 21

# Zabrodsky Lecture 2: Cohomological Field Theories

## Lecturer:

Rahul Pandharipande (ETH Zurich)
11:00am to 12:00pm

## Location:

Ross 70
Cohomological Field Theories (CohFTs) were introduced to keep track of the classes on the moduli spaces of curves defined by Gromov-Witten theories and their cousins. I will define CohFTs (following Kontsevich-Manin), explain the classification in the semisimple case of Givental-Teleman, and discuss the application to Pixton's relations which appear in the first lecture.
2018 Oct 18

# Zabrodsky Lecture 1: Geometry of the moduli space of curves

## Lecturer:

Rahul Pandharipande (ETH Zurich)
2:30pm to 3:30pm

## Location:

Manchester House, Lecture Hall 2

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. My goal is to give a presentation of the progress in the past decade and the current state of the field.

2019 Mar 11

# Combinatorics Seminar: Yuval Filmus (Technion) "Structure of (almost) low-degree Boolean functions"

11:00am to 1:00pm

## Location:

CS bldg, room B500, Safra campus, Givat Ram
Speaker: Yuval Filmus, Technion Title: Structure of (almost) low-degree Boolean functions Abstract: Boolean function analysis studies (mostly) Boolean functions on {0,1}^n. Two basic concepts in the field are *degree* and *junta*. A function has degree d if it can be written as a degree d polynomial. A function is a d-junta if it depends on d coordinates. Clearly, a d-junta has degree d. What about the converse (for Boolean functions)? What if the Boolean function is only *close* to degree d? The questions above were answered by Nisan-Szegedy, Friedgut-Kalai-Naor, and Kindler-Safra.
2018 Oct 23

# Dynamics Lunch: Amir Algom "On \alpha \beta sets."

12:00pm to 1:00pm

## Location:

Manchester faculty club
Let $\alpha, \beta$ be elements of infinite order in the circle group. A closed set K in the circle is called an \alpha \beta set if for every x\in K either x+\alpha \in K or x+\beta \in K. In 1979 Katznelson proved that there exist non-dense \alpha \beta sets, and that there exist \alpha \beta sets of arbitrarily small Hausdorff dimension. We shall discuss this result, and a more recent result of Feng and Xiong, showing that the lower box dimension of every \alpha \beta set is at least 1/2.
2019 Jan 15

# Dynamics Lunch: Tsviqa Lakrec "Recurrence properties of random walks on ﬁnite volume homogeneous manifold"

12:00pm to 1:00pm

2018 Jun 28

# Basic Notions: Barry Simon "More Tales of our Forefathers (Part II)"

4:00pm to 5:30pm

## Location:

Manchester Hall 2
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. Among the mathematicians with vignettes are Riemann, Newton, Poincare, von Neumann, Kato, Loewner, Krein and Noether.
2018 Jun 26

# Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

11:30am to 12:30pm

## Location:

Manchester House, Lecture Hall 2
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.
2018 Jun 27

# Amitsur Symposium: Tsachik Gelander - "Local rigidity of uniform lattices"

3:00pm to 4:00pm

## Location:

Manchester House, Lecture Hall 2
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in Isom(X) where X is a proper CAT(0) space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang’s finiteness theorem for certain non-positively curved metric spaces. This is a joint work with Arie Levit.
2018 Jun 27

# Amitsur Symposium: Amiram Braun - "The polynomial question in modular invariant theory, old and new"

11:30am to 12:30pm

## Location:

Manchester House, Lecture Hall 2
Let G be a finite group, V a finite dimensional G- module over a field F, and S(V) the symmetric algebra of V. The above problem seeks to determine when is the ring of invariants S(V)^G , a polynomial ring. In the non-modular case (i.e. char(F) being prime to order(G)), this was settled in the Shephard-Todd-Chevalley theorem. The modular case (i.e. char(F) divides order (G) ), is still wide open. I shall discuss some older results due to Serre, Nakajima , Kemper-Malle and explain some new results, mostly in dimension 3.