## 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 |