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.

Voting Paradoxes and Combinatorics

Noga Alon
Institute for Advanced Study, Visiting Professor
October 13, 2010

The early work of Condorcet in the eighteenth century, and that of Arrow and others in the twentieth century, revealed the complex and interesting mathematical problems that arise in the theory of social choice. In this lecture, Noga Alon, Visiting Professor in the School of Mathematics, explains how the simple process of voting leads to strikingly counter-intuitive paradoxes, focusing on several recent intriguing examples.

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.