Events & Seminars

2017 Jun 08

Wolf Prize Lecture - Rick Schoen (Stanford): The geometry of eigenvalue extremal problems

11:00am to 12:00pm

Location: 

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 which progress has been made focusing primarily on the case of surfaces with
2017 Jan 19

Special colloquium: Asaf Katz (HUJI Perlman prize) "Sparse equidistribution in unipotent flows"

4:00pm to 5:00pm

Location: 

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.
2015 Oct 22

Colloquium: Nir Avni (Northwestern), "Counting points and counting representations"

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?

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