Previous Conferences & Workshops

I will discuss a generalization of the modularity lifting theorems of Clozel, Harris and Taylor to the case of ordinary Galois representations. The result is obtained by applying the Taylor-Wiles method (with innovations due to Kisin and Taylor)...

I will discuss a recent joint work with Thomas Barnet-Lamb and Toby Gee in which we prove the Sato-Tate conjecture for non-CM regular algebraic cuspidal automorphic representations of GL_2 over a totally real field.

We improve Kolyvagin's upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and...

What do the following seven things have in common: * zero-dimensional homogeneous polynomial ideals, * multivariate polynomial interpolation, * box splines, * hyperplane arrangements, * parking functions on graphs, * f-vectors of matroids, * integer...

The Schmidt subspace theorem is a deep generalization of Roth's theorem in Diophantine approximation to the setting of hyperplanes in projective space. Another well-known generalization of Roth's theorem is the theorem of Wirsing, which extends Roth...

I will discuss several results on mean-values of multiplicative functions, notably Halasz's method for estimating such averages. In the second lecture I will show how this circle of ideas can be used to derive "weak subconvexity" bounds for L...

The PCP Theorem shows that any mathematical proof can be efficiently converted into a form that can be checked probabilistically by making only *two* queries to the proof, and performing a "projection test" on the answers. This means that the answer...