ULethbridge Number Theory and Combinatorics Seminar: Mohsen Aliabadi

In this talk, we introduce the notions of matching matrices in groups and vector spaces, which lead to some necessary conditions for existence of acyclic matching in abelian groups and its linear analogue. We also discuss the linear local matching property in field extensions to find a dimension criterion for linear locally matchable bases. We provide an upper bound for the dimension of primitive subspaces in a separable field extension.We finally provide an application of matchings about the fundamental theorem of algebra. Our tools mix combinatorics and linear algebra.