A colloquium is a broad-reaching lecture aiming to present mathematical ideas to a diverse audience, from undergraduates to faculty. It highlights general mathematical concepts in an accessible manner.
Speaker: Kari Astala, University of Helsinki
Title: Geometry of random tilings via complex structures and the Beltrami equation
Abstract: Under suitable boundary restrictions, scaling limits of random tilings present surprising geometric features: one observes definite deterministic and disordered (or frozen and liquid) limit configurations with interesting geometric properties.
In this talk we explain how the geometry of these limiting domains can all be understood and described via suitable degenerate Beltrami differential equations and the complex structures they provide.
