Title: Circle patterns on surfaces with complex projective structures
Speaker: Wai Yeung Lam (Université du Luxembourg)
Date: 30 November 2020
Time: 4:00 pm
Venue: MS teams (team code hiq1jfr)
William Thurston proposed regarding the map induced from two circle packings with the same tangency pattern as a discrete holomorphic function.
A discrete analogue of the Riemann mapping is deduced from Koebe-Andreev-Thurston theorem. A natural question is how to extend this theory to
Riemann surfaces and relate classical conformal structures to discrete conformal structures. Since circles are preserved under complex projective
transformations, one can consider circle packings on surfaces with complex projective structures. Kojima, Mizushima and Tan conjectured that for a given
combinatorics the deformation space of circle packings is diffeomorphic to the Teichmueller space via a natural projection. In this talk, we will report
progress on the torus case.