Video Lectures

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...

I will first discuss the orientability of the moduli spaces of J-holomorphic maps with Lagrangian boundary conditions. It is known that these spaces are not always orientable and I will explain what the obstruction depends on. Then, in the presence...

Legendrian contact homology (LCH) is a powerful holomorphic curves invariant for Legendrian submanifolds in contact manifolds. It is defined via a differential graded algebra (DGA), but the computation of its homology is often too difficult...

When objectivity became a goal for science in the early nineteenth century, natural philosophers had to invert epistemic virtues: idealization out, mechanical representation in. Twentieth-century scientists questioned image-based mechanical...

The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann hypothesis fails. In...