IAS Analysis Seminar Spring 2008
Tom Sanders and I jointly organized a series of analysis seminars at the Institute for Advanced Study during the Spring term of 2008. For the record, here is a list of the invited speakers and their titles and abstracts where available.
Wednesday, February 27 2008
Speaker: 
Alexander Leibman, Ohio State University. 
Title: 
Orbit of the diagonal of a power of a nilmanifold 
Abstract: 
Let p_1,...,p_k be integer polynomials of one or several variables. There is a relation between the density of polynomial configurations a+p_1(n),...,a+p_k(n) in sets of integers and the form of the closure of the diagonal of X^k under the "polynomial action" (T^{p_1},...,T^{p_k}), where X is a "universal" nilmanifold (that is, a compact homogeneous space of a "universal" nilpotent Lie group) and T is a translation of X. It is easy to describe this diagonal in the case all p_i are linear, and not easy when p_i are not linear.

Time: 
2pm 
Venue: 
Simonyi Hall S101 
Wednesday, March 12 2008
Speaker: 
Lior Silberman, Harvard University and Institute for Advanced Study. 
Title: 
Constructing Wild Groups 
Abstract: 
not available 
Time: 
2pm 
Venue: 
West Building Lecture Hall 
Wednesday, March 26 2008
No seminar due to faculty lecture by Peter Sarnak at 4:30pm in Wolfensohn Hall. 
Wednesday, April 2 2008
Speaker: 
Elon Lindenstrauss, Princeton University. 
Title: 
Stationary measures and equidistribution on the torus 
Abstract: 
In this talk I will consider actions of nonabelian groups on ndimensional tori, explain the notions of stiffness and stationary measures, and show how under fairly general assumptions stationary measures can be classified. A key ingredient is a result of Bourgain related to the sum product phenomena on the reals.
In particular, we prove the following: let A, B be two non commuting 2x2 integer matrices of determinant one. Consider a random product X_r....X_1.y where y is a point in the two torus. We show that as r> infinity this random product is distributed in an increasingly uniform manner.
Based on joint work with Bourgain, Furman and Mozes.

Time: 
10:30am Please note the unusual time. 
Venue: 
West Building Lecture Hall 
Wednesday, April 9 2008
Wednesday, April 16 2008
Speaker: 
Jean Bourgain, Institute for Advanced Study. 
Title: 
Expanders and random walks in SL(d,q) 
Abstract: 
not available 
Time: 
2pm 
Venue: 
Simonyi Hall S101 
Wednesday, April 23 2008
Speaker: 
Nikos Frantzikinakis, University of Memphis. 
Title: 
A Hardy field extension of Szemeredi's theorem 
Abstract: 
In 1975 Szemeredi proved that every subset of the integers with positive density contains arbitrarily long arithmetic progressions. Bergelson and Leibman showed in 1996 that the common difference of the arithmetic progression can be a square, a cube, or more generally of the form p(n) where p(n) is any integer polynomial with zero constant term. We produce a variety of new results of this type. We show that the common difference can be of the form [n^c] where c is any positive real number, or more generally of the form [a(n)] where a(x) is any function that belongs to some Hardy field and satisfies some mild growth conditions. This allows us for example to deal with the class of logarithmicoexponential functions, i.e., functions that can be constructed by a finite combination of the ordinary arithmetical symbols, the real constants, and the functions e^x, logx.
This is joint work with Mate Wierdl.

Time: 
2pm 
Venue: 
Simonyi Hall S101 
Wednesday, May 14 2008
Speaker: 
Ciprian Demeter, UCLA and Institute for Advanced Study. 
Title: 
On the two dimensional Bilinear Hilbert Transform and Z^2 actions 
Abstract: 
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z^2 actions. Our techniques combine novel one and a half dimensional phasespace analysis with more standard one dimensional theory. This is joint work with Christoph Thiele.

Time: 
2pm 
Venue: 
West Building Lecture Hall Please note the change of date. 
