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Texas A&M University

Events for 11/15/2021 from all calendars

Geometry Seminar

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Time: 3:00PM - 4:00PM

Location: zoom

Speaker: Tim Seynnaeve, U. Bern

Title: Enumerative geometry for algebraic statistics and semidefinite programming

Abstract: In statistics, the maximum likelihood degree of a statistical model measures the algebraic complexity of maximum likelihood estimation. In convex optimization, the algebraic degree of semidefinite programming measures the algebraic complexity of solving the KKT equations. We discovered that both of these numbers have an interpretation in terms of classical problems in enumerative geometry. To phrase it in a more modern language: they are intersection numbers on the variety of complete quadrics. As an application, we prove a conjecture by Sturmfels and Uhler stating that the maximum likelihood degree behaves polynomially. This illustrates both how methods from algebraic geometry can be used to prove conjectures arising in applications, but also how drawing inspiration from applications gives rise to new geometric questions. This talk is based on joint projects with Rodica Dinu, Laurent Manivel, Mateusz Michalek, Leonid Monin, and Martin Vodicka.