Lukasz Grabowski

Lukasz Grabowski (Lancaster University)

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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