Algebra Seminar

09/23/2020 - 2:00pm to 3:00pm
Speaker(s) / Presenter(s): 
Alessandro Neri, Technical University of Munich

Title: Spaces of matrices with high rank using Galois theory

Abstract: In this work we present an approach for studying linear spaces of n x n matrices with high rank. We do so for the case where the underlying field K admits a Galois extension L of degree n. In the special case where the Galois group is abelian, we derive the analogues of the celebrated Alon-F├╝redi theorem and of the Schwartz-Zippel lemma for endomorphisms, which produce nontrivial lower bounds on the rank of a linear endomorphism. The main motivation arises from algebraic coding theory, and in particular from the theory of rank-metric codes.

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