Previous Conferences & Workshops

In the last eight lectures, we have reduced the proof of the Bloch-Kato to an assertion about motivic cohomology operations. We will prove that this assertion is correct, and so complete the proof of the Bloch-Kato conjecture.

Originally number theoretic methods were used to construct optimal (explicit) expanders. Recently combinatorial methods have been utalized in proving that certain number theoretic graphs are expanders. We will explain some uses of such expanders in...

We develop a framework for obtaining (deterministic) Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic problems with either convex or monotone single-period cost functions. Using our framework, we give the first...

In 1957 Erdos asked what is the smallest maximum modulus of a trigonometric polynomial of degree n all whose coefficients have modulus 1. He thought that there should be a c>0 such that this max modulus is larger than (1+c)sqrt(n).In 1966 Littlewood...

Let F be a presheaf with transfers on the category of smooth affinoid varieties over a non-archemidean field. Suppose that F is overconvergent and homotopy invariant. Then the presheaves H^i(-,F) are also homotopy invariant (where the cohomology is...

I will describe a system of differential equations for the genus 0 open Gromov-Witten potential of a Lagrangian submanifold fixed by an anti-symplectic involution. These equations involve both the open Gromov-Witten potential and the closed Gromov...

Since the proof of Iwasawa's main conjecture in the classical case (theorem of Mazur and Wiles), automorphic forms on GL(2) have played an essential role to understand Iwasawa theory for GL(1). In this lecture, Leopoldt 's conjecture for totally...

Consider an arrangement of nonsingular subvarieties in a nonsingular algebraic variety. We define a compactification of the complement by replacing these subvarieties with a normal crossing divisor. This compactification is obtained by a sequence of...

In the past 2 years there has been considerable progress in the algorithmic problem of combining rankings (permutations on a ground set of "candidates") into a consensus ranking. This problem dates back to the 18th century, when the French...

In 1951 Nash proved that every game has a Nash equilibrium. The proof is non-constructive, reducing the existence of Nash equilibria to that of Brouwer fixpoints. Whether Nash equilibria can be computed efficiently had remained open. I shall outline...