Speaker: Istvan Prause

Title: Integrability of limit shapes

Abstract:
Limit shape formation is a ubiquitous feature of highly correlated statistical mechanical systems. It says that in the macroscopic limit the random system settles into a fixed deterministic limit. These geometric limit shapes often (known or conjectured to) exhibit arctic boundaries, sharp transitions from ordered (frozen) to disordered (liquid) phases. 
The guiding theme of the talk is to ask how integrability of the model is reflected in the integrability of the limit shape PDE. I'll show that for the dimer model and the isoradial 5-vertex model limit shapes have strikingly simple parametrizations in terms of the underlying conformal coordinate. The talk is based on joint work with Rick Kenyon.