Previous Conferences & Workshops

In previous work we showed that arithmetic hyperbolic 2-manifolds that are isospectral are commensurable. In this talk we discuss the proof of the generalization to dimension 3. We had previously shown that if arithmetic hyperbolic 3-manifolds are...

We consider periodic orbits of multiparameter diagonalizable actions. A simple example of such an action is the action generated by the maps x -> 2x mod 1 and x -> 3x mod 1 on R/Z. There are strong parallels between the study of these orbits and...

We will first discuss some results on generation of finite simple groups. Using the classification of finite simple grouops, one can prove the following results: Every finite simple can be generated by two elements and the probability that a pair of...

We propose a new approach to designing a strongly polynomial algorithm for linear programming. We show that linear programming on any polytope can be reduced to linear programming on an arrangement polytope. The graphs of arrangement polytopes have...

In this talk I will give an overview of joint work with M. Rapoport and T. Yang on the construction of generating series whose coefficients are the classes of special divisors and 0-cycles on the arithmetic surfaces attached to Shimura curves. These...

The Grothendieck constant of a graph is an invariant whose study, which is motivated by algorithmic applications, leads to several extensions of a classical inequality of Grothendieck. This invariant was introduced in a joint paper with Makarychev...

The polynomial Szemeredi theorem of Bergelson and Leibman states that every integer subset with positive density contains infinitely many configurations of the form x,x+p_1(n),...x+p_k(n), where p_1,...,p_k is any fixed family of integer polynomials...

During the last 10 years the results and ideas from my work on unipotent flows have been widely used and applied to various problems arising from number theory, spectral theory, ergodic theory, the theory of elliptic curves, moduli spaces, dynamics...