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Discrete Differential Geometry
January 8 – 9, 2018, San Diego, California

The emerging field of discrete differential geometry (DDG) studies discrete analogs of smooth geometric objects, providing an essential link between analytical descriptions and computation. In recent years it has unearthed a rich variety of new perspectives on applied problems in computational anatomy/biology, computational mechanics, industrial design, computational architecture, and digital geometry processing at large. The basic idea behind discrete differential geometry (DDG) is that a discrete object like a polyhedron is not merely an approximation of a smooth one, but rather a differential-geometric object in its own right. In contrast to traditional discretization which focuses on eliminating approximation error only in the limit of refinement (e.g., by taking smaller and smaller finite differences), DDG places an emphasis on so-called “mimetic” discretization where key properties of a system are guaranteed to be exactly preserved, no matter how fine or coarse the discretization. For instance, just as algorithms for simulating mechanical systems might seek to exactly preserve energy or momentum, structure-preserving discretizations of geometry might seek to exactly preserve quantities like total curvature. More broadly, DDG focuses on the discretization of differential geometric objects that do not naturally fall under the umbrella of traditional numerical analysis. This course provides an overview of recent themes in DDG, including both mathematical developments and examples of how DDG is applied in practice.

Course Organizer

Keenan Crane, Carnegie Mellon University

Lecture Topics

  • Discrete Laplace Operators, Max Wardetzky, University of Göttingen
  • Discrete Parametric Surfaces, Johannes Wallner, Technische Universität Graz
  • Discrete Mappings, Yaron Lipman, Weizmann Institute
  • Discrete Conformal Geometry, Keenan Crane, Carnegie Mellon University
  • Optimal Transportation on Discrete Domains, Justin Solomon, Massachusetts Institute of Technology

More information to be posted

Registration Information

Registration fees for this course are posted here. Registration will open no later than September 11, 2017.

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