Recent & Upcoming Talks

2024

Toward understanding semigroup properties under the tensor product(s)

In this talk, I will present some results that the late Nick Baeth and I proved about tensor products of [your favorite adjective here] semigroups. I will also outline Nick’s grand vision and our intended future directions for those interested in carrying on in Nick’s …
Nov 8, 2024 3:30 PM Syracuse University

2023

Hypergraphs Applied to Commutative Algebra, or, why prove theorems when you can draw pictures?

In this talk, we take a problem in commutative algebra (identifying an object called a nearly complete intersection ideal) and build on the well-established theory of edge ideals to come up with a graph theoretic condition to solve the problem. This sounds dry, but the talk will …
Apr 1, 2023 3:30 PM George Mason University

2021

A Hypergraph Characterization of Nearly Complete Intersections

Recently, nearly complete intersection ideals were defined by Boocher and Seiner to establish lower bounds on Betti numbers for monomial ideals (arXiv:1706.09866). Stone and Miller then characterized nearly complete intersections using the theory of edge ideals …
May 2, 2021 5:00 PM On Zoom

The Math of Online Privacy

Whether you’re buying shoes from Zappos or voting on a networked ballot box, you want to be confident that your information is verified (it really came from you!) and secure (only you and the approved second parties can see it!). Professor Gibbons will talk about the math behind …
Apr 14, 2021 3:30 PM On Zoom

2020

The Real Friends are the Betti Numbers We Calculated Along the Way

Ever wondered what your life might have been like if you chose differently in the past? This talk is about how I nearly became a geometric group theorist – until I saw homological algebra used to prove theorems about modules. My emphasis will be on what Betti numbers are, a …
Oct 8, 2020 3:30 PM On Zoom
Video

2019

Syzygy: When Submodules Align

In astronomy, a syzygy is an alignment of celestial bodies. In mathematics, a syzygy is an alignment of a kernel of one homomorphism with the image of another! In this talk I’ll introduce free resolutions, syzygies, and a few applications thereof.
Aug 3, 2019 11:00 AM Cincinnati, OH
PDF

Boij-Soederberg Theory as an Introduction to Research in Commutative Algebra

Commutative algebra is ripe with topics for undergraduate research, and I will discuss one such topic: Boij-Soederberg theory. I will focus on specific results from two undergraduate research projects I mentored in this context, including how I developed the projects to dovetail …
Jan 20, 2019 12:00 AM Baltimore, MD
PDF

2018

Syzygy: a mysterious mathematical object

From 0 to syzygy in 5 minutes!
Jul 19, 2018 3:30 PM Park City Mathematics Institute
Video

Shidoku: A Crash Course on Ideals and Varieties

It turns out that algebra is more than just x’s and torturing high school students. Algebra has been used to solve problems from biology, physics, and economics. In this talk, I’ll walk through an example of using algebra to solve a slightly less ambitious problem: …
Jun 21, 2018 12:00 AM

Recursive Decompositions of Betti diagrams of complete intersections

In this talk we introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate …
Jun 21, 2018 12:00 AM Syracuse University
PDF Code

Maximum Likelihood Degrees for Discrete Random Models

The goal of this talk is to highlight a theorem proved during the Mathematical Research Community: Algebraic Statistics summer program by the Likelihood Geometry group. This group was led by Serkan Hosten and Jose Israel Rodriguez. In the talk, I will focus on the application of …
Jun 21, 2018 12:00 AM Georgia Institute of Technology, Atlanta, GA
Slides

Googling It: How Google Ranks Search Results

Have you ever wondered how Google decides which search results are most relevant to your search query? The secret to Google’s early success was PageRank, an algorithm for scoring the relevance and popularity of websites, and the math that makes the algorithm possible is …
Jun 21, 2018 12:00 AM All Night Reading Room, Burke Library, Hamilton College, Clinton, NY
Slides Video

From 0 to Syzygy in 5 minutes

Syzygies are among the most important, useful, and beautiful objects in algebra. After this talk, you’ll have a feel for what they are and what they can do. Ignite talks are fast-paced: 20 slides at 15 seconds each
Jun 21, 2018 12:00 AM Park City Mathematics Institute, Park City, UT
Video

Gerrymandering: The Math Behind the Madness.

Just about everyone agrees that partisan gerrymandering is unfair; arguments center around how to detect it and whether there are other gerrymanders (racial, ethnic, socioeconomic) that we should be looking for, too. We will examine several mathematical criteria and metrics for …
Jun 20, 2018 12:00 AM Levitt Center Conference Room, Hamilton College, Clinton, NY
Slides