Abstract: Basic representations for three-dimensional geometry have a profound effect on what can be achieved downstream, in a variety of disciplines (physical simulation, computational design, geometric learning, etc.).  In this talk I will discuss recent efforts in our group to revisit fundamental choices in the way we represent digital geometry, and solve geometric equations.  The guiding principle is to translate deep knowledge from the continuous world (especially the field of differential geometry) into the discrete setting, rather than re-invent the wheel for each application.

Bio: Keenan Crane is the Michael B. Donohue Associate Professor of Computer Science and Robotics at Carnegie Mellon University, and a member of the Center for Nonlinear Analysis.  He is a Packard Fellow and recipient of the NSF CAREER Award, was a Google PhD Fellow in the Department of Computing and Mathematical Sciences at Caltech, and was an NSF Mathematical Postdoctoral Research Fellow (MSPRF) at Columbia University.  Dr. Crane’s work applies insights from differential geometry to build fundamental representations and algorithms for processing, designing, and analyzing geometric data.  This work has been featured in venues such as Notices of the AMS and Communications of the ACM, as well as in the popular press through outlets such as WIRED, Popular Mechanics, National Public Radio, Scientific American, and The New York Times.