## A spectral gap in $\mathrm{SL}^2(\mathbb R)$ and applications: expansion, Furstenberg measures and the Anderson-Bernoulli model

Jean Bourgain
IBM von Neumann Professor, School of Mathematics
November 30, 2016

## $C^0$ Hamiltonian dynamics and a counterexample to the Arnold conjecture

Member, School of Mathematics
November 29, 2016
After introducing Hamiltonian homeomorphisms and recalling some of their properties, I will focus on fixed point theory for this class of homeomorphisms. The main goal of this talk is to present the outlines of a $C^0$ counterexample to the Arnold conjecture in dimensions four and higher. This is joint work with Lev Buhovsky and Vincent Humiliere.

## Rectification and the Floer complex: quantizing Lagrangians in $T^*N$

Claude Viterbo
Ecole Normale Supérieure
November 29, 2016
We shall give a construction of the quantized sheaf of a Lagrangian submanifold in $T^*N$ and explain a number of features and applications.

## From matrix scaling to Brascamp-Lieb and back

Zeev Dvir
Princeton University
October 8, 2016

## A Zig-Zag Recipe in Jewish Scriptures

Omer Reingol
Stanford University
October 8, 2016