The theory of polyhedral surfaces is a very concrete special case (and testing ground) of an active mathematical terrain where differential geometry (providing the classical theory for smooth surfaces) and discrete geometry (concerned withpolytopes, simplicial complexes, etc.) meet and interact.
The goal of the Research Unit is to use and combine the quite unique local expertise in both discrete and differential geometry in order to attack fundamental problems in the area of polyhedral surfaces. Areas to which we will devote considerable joint effort - and in which we expect to make substantial progress - include the following: discrete surfaces of constant mean curvature (including minimal surfaces), discrete notions of curvature, cubical complexes (including quad-meshes and quad-surfaces), and the existence and rigidity of special kinds of polyhedral surfaces. While all of these problems have interest from the pure mathematics standpoint we adopt here, many are also motivated by questions from such diverse settings as computational geometry, mesh generation, and mathematical physics.
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