## Fall 2021

Organizers: Pierre Clare and Rob Carman

The seminar meets Wednesdays at 2pm, in Jones 302. Email us for information or to be added to the mailing list.

### Next talk (10/20)

#### Eric Swartz 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.

 11/17 Vladimir Bolotnikov TBA 11/10 $\vdots$ 11/03 $\vdots$ 10/27 $\vdots$ 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