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Thursday, 12/01/2022, Time: 11:00am – 12:15pm PT
Geometry of Dependency Equilibria

Posted: November 20, 2022 | 0 comments

Bernd Sturmfels
Professor of Mathematics, Statistics and Computer Science, University of California, Berkeley
Director of the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Location: Geology Building, Room 4660

Abstract:

An n-person game is specified by n tensors of the same format. Its equilibria are points in that tensor space. Dependency equilibria satiisfy linear constraints on conditional probabilities. These cut out the Spohn variety, named after the philosopher who introduced the concept. Nash equilibria are tensors of rank one. We discuss the real algebraic geometry of the Spohn variety and its payoff map, with emphasis on connections to oriented matroids and algebraic statistics. This is joint work with Irem Portakal.

Bio:

Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington and the Technical University Darmstadt, and an honorary doctorate in 2015 from the Goethe University Frankfurt. After postdoctoral years in Minneapolis and Linz, he taught at Cornell University, before joining UC Berkeley in 1995, where he served as Professor of Mathematics, Statistics and Computer Science. Since 2017 he is a director at the Max-Planck Institute for Mathematics in the Sciences, Leipzig. In 2018 he became Honorary Professor at Technical University Berlin and University of Leipzig. His awards include a David and Lucile Packard Fellowship, a Humboldt Senior Research Prize, the SIAM von Neumann Lecturer-ship, the Sarlo Distinguished Mentoring Award, and the George David Birkhoff Prize in Applied Mathematics. He is a fellow of the AMS and SIAM, and a member of the Berlin-Brandenburg Academy of Sciences. In 2022 he spoke at the International Congress of Mathematicians. Sturmfels mentored 60 doctoral students and numerous postdocs, and he authored 11 books and 300 research articles, in combinatorics, commutative algebra, algebraic geometry, and their applications to fields like statistics, optimization, and computational biology.

Here is a link to the slides used in the presentation.