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SIAM SAGA - Seminar on Applied Geometry and Algebra
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Date: Tuesday, April 13 at 11:00am Eastern time zone

Speaker: Jan Draisma, Bern University / Eindhoven University of Technology

Title: Infinite-dimensional geometry with symmetry

Abstract: Most theorems in finite-dimensional algebraic geometry break down in infinite dimensions---for instance, the polynomial ring C[x_1,x_2,...] is not Noetherian. However, it turns out that some results do survive when a sufficiently large symmetry group is imposed; e.g., ideals in C[x_1,x_2,...] that are preserved under all variable permutations do satisfy the ascending chain condition. This phenomenon is relevant for applications, since many algebraic models come in infinite families with highly symmetric infinitedimensional limits. Here the symmetry is typically captured by either the infinite symmetric group or the infinite general linear group. Theorems about the limit imply uniform behaviour of the members of the family. I will present older and new results in this area, along with applications to algebraic statistics, tensor decomposition, and algebraic combinatorics.

Moderator: Joachim Rosenthal, University of Zurich
May 11, 2021 11:00 AM
Jun 8, 2021 11:00 AM
Jul 13, 2021 11:00 AM
Aug 10, 2021 11:00 AM
Sep 14, 2021 11:00 AM
Oct 12, 2021 11:00 AM
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Speakers

Jan Draisma
@Bern University / Eindhoven University of Technology
Jan Draisma did his Ph.D. at Eindhoven University of Technology (TU/e) in 2002 and a postdoc at Basel University before returning to TU/e as a faculty member from 2005-2016. Currently, Draisma holds the chair of algebra at Bern University, while remaining a part-time professor of applied algebra and geometry at TU/e.