Algebra & Discrete Mathematics Seminar
Spring 2017 Schedule

Location: ABEN 215
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
Previous Semesters

28 March 2017

Corey Vorland:
Homomesy for $$J([2] \times [a] \times [b])$$ and multidimensional recombination

Abstract: The actions of rowmotion and promotion on order ideals of a poset have generated a significant amount of interest in recent algebraic combinatorics research. One property associated to rowmotion and promotion that might suggest a poset is "nice" is the homomesy property. In this talk, we will discuss homomesy on the product of chains poset using a beautiful technique called recombination.

21 March 2017

Jim Coykendall
(Clemson University): CK-Domains and a Strong Noetherian Property

Abstract: A CK (Cohen-Kaplansky) domain is an atomic integral domain that contains only finitely many irreducible elements. Of course, PIDs with only finitely many primes are examples, but there are myriad other examples (e.g. if $$F$$ is a finite field then any proper subring of $$F[x]$$ generated over $$F$$ by powers of $$x$$ is a CK domain that is not a PID). We will consider some examples and give some relevant (and reasonably new) results on CK-domains. From there we will see how this class of rings naturally segues into a class of domains with a condition that is stronger than the Noetherian property. And in fact, this property lends itself nicely to (certain aspects of) topology.

14 February 2017

Jessica Striker:
Juggling and the stationary state distribution

Abstract:
In a discrete dynamical system, such as a random juggling pattern, a natural question is to find the probability that the system will be in a given state after running for a long time. This is called the stationary state distribution. In this expository talk, I’ll show how to compute the stationary state distribution for random juggling patterns, using only linear algebra, and then mention an idea for a related research project.