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.
|10/20||Eric Swartz||Covering numbers of rings with unity (Slides)|
|10/06||Gabriel Martins (Sacramento State)||Skateboard tricks and topological flips (Slides)|
|9/29||Cordelia Li'22||Copositive matrices, their dual, and the Recognition Problem (Slides)|
|9/22||Merielyn Sher'22||Enumerating minimum path covers of trees (Slides)|
|9/15||Bjoern Muetzel (Eckerd College)||Harmonic forms on pinched surfaces (Slides)|
|9/08||Gexin Yu||Sufficient conditions for 2-dimensional graph rigidity|