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 â€¦

Whether youâ€™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 â€¦

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 â€¦

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.

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 â€¦

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: â€¦

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 â€¦

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 â€¦

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 â€¦

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*

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 â€¦

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