PIMS MSS Colloquium: Stefan Steinberger

  • Date: 02/02/2023
  • Time: 14:00
Stefan Steinberger, University of Washington

University of Alberta


How curved is a combinatorial graph?


Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as manifolds and a number of different notions of curvature have been proposed. I will introduce some of the existing ideas and then propose a new notion based on a simple and explicit linear system of equations that is easy to compute. This notion satisfies a surprisingly large number of desirable properties -- connections to game theory (especially the von Neumann Minimax Theorem) and potential theory will be sketched; simultaneously, there is a certain "magic" element to all of this that is poorly understood and many open problems remain. I will also sketch some curious related problems that remain mostly open. No prior knowledge of differential geometry (or graphs) is required.

Other Information: 

Location: CAB 235


Time: 3pm Mountain/ 2pm Pacific