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Talk

Higher-distance commuting varieties

  • Ralph Morrison (Williams College)
G3 10 (Lecture hall)

Abstract

The commuting variety is a well-studied object in algebraic geometry whose points are pairs of matrices that commute with one another. In this talk I present a generalization of the commuting variety by using the notion of commuting distance of matrices, which counts how many nonscalar matrices are required to form a commuting chain between two given matrices. I will prove that over any algebraically closed or real closed field, the set of pairs of matrices with bounded commuting distance forms an affine variety. I will also discuss many open problems about these varieties, and present preliminary results in these directions. This is based on joint work with Madeleine Elyze and Alexander Guterman.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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