What is Discrete Differential Geometry?

Monday, June 17, 2019 - 11:30am - 12:30pm
Keller 3-180
Peter Schroeder (California Institute of Technology)
Differential geometry has historically been conceived and studied in the smooth setting. Much can be learned this way. Yet, when it comes to computation and the many problems and questions which can only be accessed through computation we must leave the ideal world of infinitely differentiable objects and descend to the finite dimensional world a computer can deal with. Thus enters Discrete Differential Geometry. What are appropriate notions of, for example, curvatures in the discrete setting of polylines of triangle (surface) meshes? Should we just discretize in the sense of numerical analysis? Or are there ways to define these notions discretely such that desirable properties from the smooth setting continue to hold?