Conformal Geometry from circle packings

Speaker：Wai Yeung Lam

Date：Tues. & Thurs. 2021-02-22~05-16，13:30-15:05

Venue：BIMSA 1120 Room & Zoom ID：388 528 9728 Password：BIMSA

Abstract：

In the classical theory, holomorphic functions are conformal, mapping infinitesimal circles to themselves. Instead of infinitesimal size, a circle packing is a configuration of finite-size circles where certain pairs are mutually tangent. William Thurston proposed regarding a map induced from two circle packings with the same tangency pattern as a discrete holomorphic function, which leads to a rich theory of discrete conformal geometry. Throughout the course, we will explore its connection to the classical Teichmüller theory and hyperbolic geometry.

Prerequisite:

Complex analysis

References:

K. Stephenson. Introduction to circle packing. Cambridge University Press, Cambridge, 2005. The theory of discrete analytic functions.