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Approximation of groups with respect to the rank metric

Speaker(s)
Łukasz Grabowski
Affiliation
Lancaster University
Date
June 11, 2019, 4:15 p.m.
Room
room 3180
Seminar
Seminar Algebraic Topology

Abstract: I'll talk about an ongoing joint work with Gabor Elek about approximation of groups with respect to the rank metric. The basic question is the following variant of the Halmos problem about commuting matrices: if A and B are large matrices such that the rank of the image of the commutator is small, is it true that A and B can be perturbed with small rank matrices in such a way that the resulting matrices commute? There are interesting connections to classical notions of commutative algebra, in particular we develop what are perhaps some new (or forgotten) variants of Nullstellensatz for primary ideals.