School of Mathematics

Metaphors in Systolic Geometry

Larry Guth
University of Toronto; Institute for Advanced Study
October 18, 2010

The systolic inequality says that if we take any metric on an n-dimensional torus with volume 1, then we can find a non-contractible curve in the torus with length at most C(n). A remarkable feature of the inequality is how general it is: it holds for all metrics.

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

The Fundamental Curve of p-Adic Hodge Theory

Jean-Marc Fontaine
University of Paris-Sud 11; Institute for Advanced Study
October 14, 2010

The Completed Cohomology of Arithmetic Groups

Frank Calegari
Northwestern University; Member, School of Mathematics
October 13, 2010

Descriptions of the Grain-Growth Structure

Jeremy Mason
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.