Description:

Structure preserving discretizations in geometry and mathematical physics - Discrete conformal mappings and their generalizations: circle patterns, discrete conformal equivalence, hyperbolic structures, ring patterns. Applications to differential geometry of surfaces (discrete minimal and constant mean curvature surfaces), computer graphics (texture mappings) and integrable models of mathematical physics. Partially based on modern research with presentation of open problems.

Prerequisite: Complex analysis

Reference:

There will be a script of lectures available and references to research literature.

In particular:

A.I. Bobenko, Yu.B. Suris, Discrete differential geometry: Integrable structure, Graduate Studies in Math. 98, AMS, 2008

A.I. Bobenko, U. Pinkall, B. Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, Geometry and Topology 19 (2015) 2155-2215

A.I. Bobenko, T. Hoffmann, B.A. Springborn, Minimal surfaces from circle patterns: Geometry from combinatorics, Ann. of Math. 164:1 (2006) 231-264

Target Audience: Graduate students, and Undergraduate students with knowledge of complex analysis

Teaching Language: English

Registration: https://www.wjx.top/vm/whYGwxM.aspx#

Bio: Professor of Technische Universitaet Berlin, Germany. Head of the DFG-Collaborative Research Center “Discretization in Geometry and Dynamics”, PhD: Steklov Math. Institute, Russia.