Recent & Upcoming Talks

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 …

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.

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 …

2018

Syzygy: a mysterious mathematical object

From 0 to syzygy in 5 minutes!

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: …

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 …

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 …

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 …

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

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 …