2018 Dec 31

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

2:00pm to 3:00pm

## 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
2019 Mar 11

# Arindam Banerjee, TBA

11:00am to 12:30pm

2019 Jan 15

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

12:00pm to 1:00pm

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.
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 27

# Amitsur Symposium: Elyiahu Rips - "Free Engel groups" (joint work with Arye Juhasz)

10:00am to 11:00am

## Location:

Manchester House, Lecture Hall 2
A free n-Engel group is the relatively free group of the variety of groups with the identical relation [x, y, y,...,y (n times)]=1. Let n>=20. We show that the free Engel group on at least two generators is not locally nilpotent. Our approach to Engel groups combines
2018 Jun 26

# Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"

3:00pm to 4:00pm

## Location:

Manchester House, Lecture Hall 2
The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s. Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.
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.
2018 Jun 26

# Amitsur Symposium: Lev Glebsky - "Approximations of groups by finite and linear groups"

4:30pm to 5:30pm

## Location:

Manchester House, Lecture Hall 2
The sofic groups and hyperlinear groups are groups approximable by finite symmetric and by unitary groups, respectively. I recall their definitions and discuss why those classes of groups are interesting. Then I consider approximations by other classes of groups and review some results, including rather recent ones by N. Nikolov, J. Schneider, A.Thom, https://arxiv.org/abs/1703.06092 . If time permits I'll speak about stability and its relations with approximability.