Seminars

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"

2:00pm 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 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.

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 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.

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