Members Seminar: The Role of Symmetry in Phase Transitions

The Role of Symmetry in Phase Transitions - Tom Spencer

Tom Spencer
Professor, School of Mathematics, Institute for Advanced Study
January 23, 2012

This talk will review some theorems and conjectures about phase transitions of interacting spin systems in statistical mechanics. A phase transition may be thought of as a change in a typical spin configuration from ordered state at low temperature to disordered state at high temperature. I will illustrate how the symmetry of a spin system plays a crucial role in its qualitative behavior. Of particular interest is the connection between supersymmetric statistical mechanics and the spectral theory of random band matrices.