2014
Mar
13

# Ostrover

2:30pm to 3:30pm

2014
Mar
13

2:30pm to 3:30pm

2013
Oct
31

2:30pm to 3:30pm

2017
Jun
08

11:00am to 12:00pm

Levin building, lecture hall 8

Title: “The geometry of eigenvalue extremal problems”

Abstract: When we choose a metric on a manifold we determine the spectrum of

the Laplace operator. Thus an eigenvalue may be considered as a functional

on the space of metrics. For example the first eigenvalue would be the fundamental

vibrational frequency. In some cases the normalized eigenvalues are bounded

independent of the metric. In such cases it makes sense to attempt to find

critical points in the space of metrics. In this talk we will survey two cases in

Abstract: When we choose a metric on a manifold we determine the spectrum of

the Laplace operator. Thus an eigenvalue may be considered as a functional

on the space of metrics. For example the first eigenvalue would be the fundamental

vibrational frequency. In some cases the normalized eigenvalues are bounded

independent of the metric. In such cases it makes sense to attempt to find

critical points in the space of metrics. In this talk we will survey two cases in

2013
Dec
12

2:30pm to 3:30pm

2014
Feb
20

2:30pm to 3:30pm

2017
Jan
19

4:00pm to 5:00pm

Manchester building room 2

Abstract - Equidistribution problems, originating from the classical works of Kronecker, Hardy and Weyl about equidistribution of sequences mod 1, are of major interest in modern number theory.

We will discuss how some of those problems relate to unipotent flows and present a conjecture by Margulis, Sarnak and Shah regarding an analogue of those results for the case of the horocyclic flow over a Riemann surface. Moreover, we provide evidence towards this conjecture by bounding from above the Hausdorff dimension of the set of points which do not equidistribute.

We will discuss how some of those problems relate to unipotent flows and present a conjecture by Margulis, Sarnak and Shah regarding an analogue of those results for the case of the horocyclic flow over a Riemann surface. Moreover, we provide evidence towards this conjecture by bounding from above the Hausdorff dimension of the set of points which do not equidistribute.

2014
Jun
12

2:30pm to 3:30pm

2014
Mar
20

2:30pm to 3:30pm

2015
Oct
22

2:30pm to 3:30pm

Title: Counting points and counting representations

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?

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?

2014
May
22

2:30pm to 3:30pm

2014
Jan
16

2:30pm to 3:30pm

2014
Feb
27

2:30pm to 3:30pm

2013
Nov
14

2:30pm to 3:30pm

2013
Dec
26

2:30pm to 3:30pm

2014
May
01

2:30pm to 3:30pm