## Even Galois Representations and the Fontaine-Mazur conjecture

Frank Calegari
Northwestern University; Institute for Advanced Study
October 14, 2010

## Lecture 1

Pierre Colmez
National Center for Scientific Research; Institute for Advanced Study
October 14, 2010

## Symplectic Homogenization

Claude Viterbo
Ecole Polytechnique; Institute for Advanced Study
October 11, 2010

Given a Hamiltonian on $T^n\times R^n$, we shall explain how the sequence of suitably rescaled (i.e. homogenized) Hamiltonians, converges, for a suitably defined symplectic metric. We shall then explain some applications, in particular to symplectic topology and invariant measures of dynamical systems.

## The Nonlinear Schroedinger Equation (NLSE) with a Random Potential: Effective Noise and Scaling Theory

Shmuel Fishman
Technion, Haifa, Israel
September 22, 2010

## Imaging of Small Inhomogeneities, Homogenization and Super Resolution

Yves Capdeboscq
University of Oxford; Institute for Advanced Study
October 8, 2010