This semester all talks will be virtual events. 30 minutes before the talk there will be an opportunity to meet the speaker. The Zoom link is https://southalabama.zoom.us/j/93680300268. Everyone is welcome to join us!
|Thursday, November 12, 2020 at 3:30 p.m.||Selvi Kara, University of South Alabama||
Monomial Ideals of Graphs
Given a homogeneous ideal I in a polynomial ring R=k[x1,…,xn], we can describe the structure of I by using its minimal free resolution. All the information related to the minimal free resolution of I is encoded in its Betti numbers. However, it is a difficult problem to express Betti numbers of any homogeneous ideal in a general way. Due to this difficulty, it is common to focus on coarser invariants of I or particular classes of ideals.
In this talk, we consider monomial ideals associated to graphs. We will discuss the Castelnuovo-Mumford regularity, projective dimension, and extremal Betti numbers of such ideals and provide formulas for these invariants in terms of the combinatorial data of their associated graphs. Results presented in this talk are from joint work with Biermann, O’Keefe, Lin, and Casiday.
|Thursday, October 22, 2020||Victor Moll, Tulane University||
A New Approach to Wallis’ Integral
The theory of differentiation is based on a small number of well-defined rules. Given a class of special functions, it is possible to use these rules to obtain all derivatives of the functions in the class. On the other hand, there is no universal algorithm for integration. It is a priori unclear why the integral of Exp(-x2) is difficult to obtain.
The talk will present a new algorithm developed in the context of integrals coming from Feynman diagrams. It consists of a small number of rules that, up to now, has produced a large number of evaluations. Most of these rules are heuristics. The analysis and proofs related to them are open questions. The method will be illustrated with Wallis’ integral, one of the first examples of a closed-evaluation.
The talk will also include interesting mathematical questions that have appeared in our study of definite integrals.
|Thursday, October 15, 2020||Steven Clontz, University of South Alabama||
Technology and the Abstract Mathematician
While my research program is disjoint from the computational side of mathematics, that does not mean my work as both a scholar and instructor isn't benefited from clever use of technology. In this talk I'll demonstrate several of my favorite tools that make my work more efficient, buying me more time for doing math. Note that each tool I'll demonstrate has a free version hosted "in the cloud", that is, all that's required is an updated web browser and internet connection to use.
|Thursday, September 24, 2020||Dan Silver, University of South Alabama||
Stop Me If You’ve Heard This Theorem Before
Mathematics is the basis of comedy. In this talk we will back up this seemingly preposterous claim. The only prerequisite is a sense of humor. There will be one performance only.