# CMU Algebra and Combinatorics Seminar

## Fall 2015

### Meeting Times

Wednesdays, 4–5pm, in Pearce 223.

### Schedule

 Date Speaker Affiliation Title 9/30 Lisa DeMeyer Central Michigan University Graph constructions associated to a semigroup 10/14 Gabriel Feinberg Haverford College Geometry, representation theory, and voting 10/21 Travis Scrimshaw University of Minnesota TBD 10/28 11/4 Andrei Minchenko Weizmann Institute TBD 11/11 Kenneth Barrese University of California, San Diego TBD 11/18 George Grossman Central Michigan University TBD 12/2 Emily Gunawan University of Minnesota Cluster Algebras from Surface Triangulations 12/9 Mark Pengitore Purdue University TBD

### Abstracts

Speaker: Lisa DeMeyer (Central Michigan University)
Title: Graph constructions associated to a semigroup
Abstract: Given a commutative semigroup $S$ with $0$, the zero divisor graph $\Gamma(S)$ is a graph whose vertices are labeled by the non-zero zero divisors of $S$ and two distinct vertices are adjacent precisely when the product of the corresponding elements in $S$ is $0$. This construction has been widely studied over the past 20 years. Elementary aspects of the relationship between $S$ and $\Gamma(S)$ will be discussed. Recent and not-so-recent results on the clique homology of $\Gamma(S)$ will be presented. The talk will conclude with a brief mention of other fruitful graph constructions associated to $S$ in the current literature.

Speaker: Gabriel Feinberg (Haverford College)
Title: Geometry, representation theory, and voting
Abstract: How much impact does the voting method have on the outcome of an election? Given some common-sense desired characteristics for a system, can we find an "ideal" election process? The answers to these questions, while potentially troubling, are established. In this talk, I'll introduce a geometric approach of Donald Saari, which leads naturally to these answers. We'll then see how a voting procedure can be considered as a $\mathbb{Q}S_n$-module homomorphism. Following the work of Michael Orrison et al., we'll exploit the well-studied representation theory of the symmetric group to make further observations.

Speaker: Travis Scrimshaw (University of Minnesota)
Title: TBD
Abstract: Coming soon …

Speaker: Andrei Minchenko (Weizmann Institute)
Title: TBD
Abstract: Coming soon …

Speaker: Kenneth Barrese (University of California, San Diego)
Title: TBD
Abstract: Coming soon …

Speaker: George Grossman (Central Michigan University)
Title: TBD
Abstract: Coming soon …

Speaker: Emily Gunawan (University of Minnesota)
Title: Cluster Algebras from Surface Triangulations
Abstract: Coming soon …

Speaker: Mark Pengitore (Purdue University)
Title: TBD
Abstract: Coming soon …