# Counting points and counting representations

Seminar

Speaker

Prof. Nir Avni (Northwestern University)

Date

04/11/2015 - 11:30 - 10:30Add to Calendar

`2015-11-04 10:30:00``2015-11-04 11:30:00``Counting points and counting representations``I will talk about the following questions: 1) Given a system of polynomial equations with integer coefficients, how many solutions does it have in the ring Z/N? 2) Given a polynomial map f:R^a-->R^b and a smooth, compactly supported measure m on R^a, does the push-forward of m by f have bounded density? 3) Given a lattice in a higher rank Lie group (say, SL(n,Z) for n>2). How many d-dimensional representations does it have? I will explain how these questions are related to the singularities of certain varieties. Along the way, I'll talk about canonical singularities, random commutators, and the moduli space of local systems. This is a joint work with Rami Aizenbud``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room

Abstract

I will talk about the following questions:

1)

Given a system of polynomial equations with integer coefficients, how many solutions does it have in the ring Z/N?

2) Given a polynomial map f:R^a-->R^b and a smooth, compactly supported measure m on R^a, does the push-forward of m by f have bounded density?

3) Given a lattice in a higher rank Lie group (say, SL(n,Z) for n>2). How many d-dimensional representations does it have?

I will explain how these questions are related to the singularities of certain varieties. Along the way, I'll talk about canonical singularities, random commutators, and the moduli space of local systems.

This is a joint work with Rami Aizenbud

Last Updated Date : 06/10/2015