Analysis and its Applications Seminar

Discrete Conformal and Harmonic Maps for Surface Analysis

When

12:30 p.m., Feb. 26, 2019

Speaker

Abstract

Conformal and harmonic maps have many nice properties, many due to the fact that they are solutions of elliptic PDE. We will briefly describe some applications and potential applications of conformal and harmonic mappings of domains and surfaces. We will also describe some techniques of discretizing these mappings in a way that preserves some geometric structure. The eventual goal is to have a robust theory of discrete mappings that maintain nice geometric properties to enable efficient computation and robustness of approximation. We will draw some connections between discrete geometry (e.g., Delaunay triangulations) and numerical analysis (e.g., finite element methods).