Covering numbers of rings with unity

Abstract: Given an algebraic structure (group, ring, etc.), a cover is defined to be a collection of proper substructures (e.g., subgroups, subrings, etc.) whose set theoretic union is the whole structure. Assuming such an algebraic structure has a cover, its covering number is defined to be the size of a minimum cover. I will discuss the rich history of this problem as well as recent joint work with Nicholas Werner on the covering number of a ring with unity. No prior knowledge will be assumed beyond the basic definitions of groups and rings.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasprobabilityquantum algebrarings and algebrasrepresentation theory

Audience: undergraduates

GAG seminar

Series comments: Description: Non-specialized research seminar