This page list all events and seminars that take place in the department this week. Please use the form below to choose a different week or date range.

## Non-commutative Analysis Seminar

### Generalized Powers’ averaging for commutative crossed products

Oct 26, 11:00—12:00, 2021, seminar room -101

#### Speaker

Tattwamasi Amrutam (BGU)

#### Abstract

In 1975, Powers proved that the free group on two generators is a $C^{\star}$-simple group. The key insight in Powers’s proof of the $C^\star$-simplicity is that the left regular representation of $\mathbb{F}_2$ satisfies Dixmier type averaging property. Using the pioneering work of Kalantar-Kennedy, it was shown by Haagerup and Kennedy independently that the $C^\star$-simplicity of the group $\Gamma$ is equivalent to the group having Powers’ averaging property. In this talk, we introduce a generalized version of Powers’ averaging property for commutative crossed products. Using the notion of generalized Furstenberg boundary introduced by Kawabe and Naghavi (independently), we show that the simplicity of the commutative crossed products $C(X)\rtimes_r\Gamma$ (for minimal $\Gamma$-spaces $X$) is equivalent to the crossed product having generalized Powers’ averaging. As an application, we will show that every intermediate $C^\star$-subalgebra $\mathcal{A}$ of the form $C(Y)\rtimes_r\Gamma\subseteq\mathcal{A}\subseteq C(X)\rtimes_r\Gamma$ is simple for an inclusion $C(Y)\subset C(X)$ of minimal $\Gamma$-spaces whenever $C(Y)\rtimes_r\Gamma$ is simple. This is a joint work with Dan Ursu.

## Colloquium

### Integral geometry and valuation theory in pseudo-Riemannian spaces

Oct 26, 14:30—15:30, 2021, Math -101

#### Speaker

Dmitry Faifman (Tel Aviv University)

#### Abstract

We will discuss the Blaschke branch of integral geometry and its manifestations in pseudo-Riemannian space forms. First we will recall the fundamental notion of intrinsic volumes, known as quermassintegrals in convex geometry. Those notions were extended later to Riemannian manifolds by H. Weyl, who discovered a remarkable fact: given a manifold M embedded in Euclidean space, the volume of the epsilon-tube around it is an invariant of the Riemannian metric on M. We then discuss Alesker’s theory of smooth valuations, which provides a framework and a powerful toolset to study integral geometry, in particular in the presence of various symmetry groups. Finally, we will use those ideas to explain some recent results in the integral geometry of pseudo-Riemannian manifolds, in particular a collection of principal Crofton formulas in all space forms, and a Chern-Gauss-Bonnet formula for metrics of varying signature. Partially based on joint works with S. Alesker, A. Bernig, G. Solanes.

## אשנב למתמטיקה

### מהלך מקרי על הילוכים מקרייםOnline

Oct 26, 18:10—19:30, 2021, בניין 32 חדר 309 וכן במרשתת

אריאל ידין

#### Abstract

נציג את המושג של הילוך מקרי, ונספר על חלק מהתוצאות הקשורות למושג זה.

נקודת ההתחלה שלנו היא משפט של Polya שמוכיח שאדם שיכור יחזור מתישהו לביתו, אבל טייס חללית שיכור יעלם לנצח בהסתברות סבירה. בהתאם לזמן, נתאר את הקשרים לרשתות חשמליות ואולי גם לתורת חבורות גיאומטרית.

אשתדל שהכל יהיה נגיש לתלמידי שנה ב ומעלה.

## AGNT

### TBA

Oct 27, 16:00—17:15, 2021, -101

none