Algebra and Combinatorics Seminar

Date: December 2, 2022

Time: 3:00PM - 4:00PM

Location: BLOC302

Speaker: Jan Draisma, Universitat Bern, Switzerland

Title: A tensor restriction theorem over finite fields

Abstract: The theorem in the title says that tensors of a fixed format over a fixed finite field K are well-quasi-ordered by restriction: they contain no infinite anti-chains. The same holds, more generally, for "tensors" in spaces described by any finite-length functor from the category of finite-dimensional K-vector spaces to itself. I will discuss several equivalent versions and consequences of the tensor restriction theorem, and explain what their proof reveals about the coarse structure of arbitrary restriction-closed tensor properties. I will also comment on analogous results for Zariski-closed tensor properties over infinite fields, which were obtained earlier in collaborations with Bik, Eggermont, and Snowden. (Based on joint work with Andreas Blatter and Filip Rupniewski: https://urldefense.com/v3/__https://arxiv.org/abs/2211.12319__;!!KwNVnqRv!CNJ4FaC_L_qPuDq9G0SSEEvvfBB16nXYFdC5foDxs-WtoqwWfZQ_EjR6RiKm7A_-Gq1IN2ghldDEZ2BAeVyhTD0$)