Previous Conferences & Workshops

I will discuss relatively new kinds of zeta and L-functions - the Ihara-Selberg-Artin L-functions attached to finite graph coverings. In joint work with Harold Stark, we have found that many of the methods used by number theorists in investigations...

Consider an affine building of type $A_n$-tilde, which is a simplicial compex of dimension $n$. For $n=1$, this is a tree, which we will require to be homogeneous. Consider the space of complex valued functions on the vertices of the building, and...

I will present a recent result by Martin Kassabov, which answers affirmatively a 20 year-old open question: Do the symmetric groups S_n contain bounded-size generating sets U_n such that the Cayley graphs C(S_n,U_n) are (bounded-degree) expander...

Let F be a finite field. The Nottingham group N(F) is the group of formal power series \{ t(1+a_1 t + a_2 t^2 + ...): a_i \in F \}or, equivalently, the group of wild automorohisms of the local field F((t)). In spite of such a simple definition, the...

In joint work with Barry Mazur, we obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields, giving evidence for a generalized Parity Conjecture. Heegner points can account for large Selmer groups in dihedral...

Unique games were introduced by Uriel Feige and Laszlo Lovasz. We are given a graph G, a set of labels [k] = {1,...,k}, and permutations pi_{uv} on the set [k] (for all edges (u,v)). Our goal is to find an assignment of labels to variables x(u) (for...

We will describe some recent ergodic theorems for general families of averages on semisimple Lie groups, and explain how they can be used to 1) Solve the lattice point counting problem for general domains in the group, with explicit estimate of the...

Let K be an imaginary quadratic field. Modular forms for K are related to the cohomology of arithmetic 3-manifolds. By using the Galois representations associated to such forms we produce an explicit tower of rational homology three spheres with...

Consider an affine building of type $A_n$-tilde, which is a simplicial compex of dimension $n$. For $n=1$, this is a tree, which we will require to be homogeneous. Consider the space of complex valued functions on the vertices of the building, and...

I will present a recent result by Martin Kassabov, which answers affirmatively a 20 year-old open question: Do the symmetric groups S_n contain bounded-size generating sets U_n such that the Cayley graphs C(S_n,U_n) are (bounded-degree) expander...