### Approximation of groups with respect to the rank metric

Algebra and Geometry Seminar

5th June 2019, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

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.

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