Researcher ORCID Identifier


Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Mohamed Omar

Reader 2

Francis Edward Su

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© 2023 Tomás Aguilar-Fraga


In combinatorics, it is often desirable to show that a sequence is unimodal. One method of establishing this is by proving the stronger yet easier-to-prove condition of being log-concave, or even ultra-log-concave. In 2019, Petter Brändén and June Huh introduced the concept of Lorentzian polynomials, an exciting new tool which can help show that ultra-log-concavity holds in specific cases. My thesis investigates these Lorentzian polynomials, asking in which situations they are broadly useful. It covers topics such as matroid theory, discrete convexity, and Mason’s conjecture, a long-standing open problem in matroid theory. In addition, we discuss interesting applications to known combinatorial objects and possible future paths for discovery.

Final Presentation.pdf (484 kB)
Final Presentation

Aguilar-Fraga Thesis Poster.pdf (177 kB)