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Conference Program

The conference will be held all day on Saturday, December 7, 2024. All events will be held in the Dolan School of Business (DSB). For directions, click on Directions above.

8:30 - 9:00am
Outside DSB 101 		Registration
9:00 - 9:10am
DSB 101 		Opening Remarks
9:10 - 10:00am
DSB 101 		Combinatorics of skew lines and geproci sets
Brian Harbourne (U. Nebraska, Lincoln)
Combinatorists have been interested in skew lines in 3 dimensional space over a finite field for a long time. Recently it has been noticed that finite sets of skew lines in 3 dimensional (projective) space over any field have a groupoid structure. This raises new combinatorial questions. It also turns out that this groupoid structure is closely related to the newly introduced algebro-geometric notion of geproci sets. This talk will discuss old and new problems in combinatorics and their connections to geproci sets.
10:10 - 11:00am
DSB 101 		From Interpolation Problems to Matroids
Paolo Mantero (U. Arkansas)
Interpolation problems are long-standing problems at the intersection of several areas of mathematics. They aim at understanding the set of all polynomial equations passing through a given finite set X of points with given multiplicities. In this talk we discuss the problem for matroidal configurations, i.e. sets of points arising from the strong combinatorial structure of a matroid. Starting from the special case of uniform matroids, we will discover how an interplay of commutative algebra and combinatorics allows us to solve interpolation problems for all matroidal configurations.
11:00 - 11:20am
Outside DSB 101 		Coffee & Tea Break
11:20 - 12:10pm
DSB 101 		Divisibility and Weaker Notions of the ACCP
Felix Gotti (Massachusetts Institute of Technology)
We can use (principal) ideal theory as a convenient alternative framework to approach questions about divisibility in commutative rings and monoids. In this talk, we will discuss some recent progress on ascending chains of principal ideals in the settings of commutative monoids and integral domains. Our primary focus will be on the almost and quasi-ACCP, which are two generalizations of the ACCP (i.e., the ascending chain condition on principal ideals), which is a well-studied condition in ideal theory. Both generalizations are based on the existence of certain common divisors for finite sets, and so they are naturally related to divisibility theory. We will highlight some recent progress on these two variations of the ACCP in connection to factorization theory.
12:10 - 1:15pm
Dolan Event Hall - Side B 		Lunch
Assorted sandwiches and wraps.
1:15 - 2:00pm
DSB 101 		Graduate Student Panel
Panelists:
Henry Potts-Rubin (U. Syracuse)
Dalena Vien (Bryn Mawr College)

Moderator:
Lingran Zhang (Fairfield University)
For undergraduate and graduate students to find out more about graduate programs, selecting an advisor, working on a dissertation, etc.
2:10 - 3:00pm
DSB 101 		Monomial Ideals Arising from Graphs: Edge and Cover Ideals
Selvi Kara (Bryn Mawr College)
In this talk, we will explore two types of monomial ideals arising from graphs: edge ideals and cover ideals. Our goal is to understand the structural properties of these ideals through their associated graphs and to identify common features shared by edge and cover ideals, while also investigating each class independently. We will focus on the Hilbert series of these ideals and a related polynomial, known as the h-polynomial, to reveal deeper algebraic and graph theoretical connections.
3:10 - 4:00pm
DSB 101 		Loewy lengths of modules of finite projective dimension
Josh Pollitz (Syracuse University)
It has been known for some time that the existence of nonzero modules of finite length and finite projective dimension force certain restrictions on the singularity of a local ring. For example, a consequence of the New Intersection theorem is that such a module exists if and only if the ring is Cohen-Macaulay. There has been a great deal of work on understanding the length/Loewy length of such modules, as any lower bounds act as numerical obstructions to the ring having “nice" singularities. In this talk, I will discuss what is already known regarding such lower bounds, and I will present some new results from joint work with Nawaj KC for lower bounds on the Loewy lengths of nonzero modules of finite projective dimension.
4:10 - 5:00pm
DSB 101 		The Plethysm Coefficients
Rosa Orellana (Dartmouth College)
The plethysm problem is a fundamental and longstanding open problem in algebraic combinatorics and representation theory. It seeks to understand the decomposition of the plethysm (composition) of two Schur functions $s_\lambda$ and $s_\mu$, denoted $s_\lambda[s_\mu]$, which itself is a symmetric function. The central problem is to find a combinatorial interpretation of the coefficients in the expansion of $s_\lambda[s_\mu]$ as a linear combination of Schur functions: \[ s_\lambda[s_\mu] = \sum_\nu a_{\lambda,\mu}^\nu s_\nu .\] Since Schur functions correspond to characters of the general linear group, the plethysm problem can also be framed as the decomposition of the composition of general linear group representations into irreducible representations. In this talk, I will introduce plethysm and present an approach to finding a combinatorial interpretation for the coefficients $a_{\lambda,\mu}^\nu$ when $\mu = (m)$ is a single-row partition. Additionally, I will discuss connections between this problem and symmetric chain decompositions of the finite Young lattice. This presentation will be accessible and introductory, aimed at a graduate student audience.
5:00 - 5:10pm
DSB 101 		Closing Remarks