Promise Prize Winners

#### 2024

The 2024 Benedict Freedman Prize for Mathematical Promise was awarded to **NATE HALL**, a mathematics and computer science major at Occidental College. Nate’s research project surrounds how graphs behave when represented in space, specifically investigating which graphs can be drawn on the standard torus without containing a pair of linked cycles. In collaboration with Professor Naimi, he found that any toroidal graph of order 8 or below that has a linkless embedding in 3D space also has one in the torus. In the coming months, he plans to extend this result to higher orders, as well as apply to graduate programs in mathematics.

#### 2023

The 2023 Benedict Freedman Prize for Mathematical Promise was awarded to **MEGHAN LEE**, a math major at Occidental College. At Kansas State University’s Summer 2022 Math REU, she worked with Dr. David Yetter and fellow students to research quandles — algebraic structures that encode a complete invariant for classical knots up to orientation reversal. The main results of her research project, “Complementation of Subquandles,” included a complete classification of subquandles whose set-theoretic complements are also subquandles, a partial transitivity criterion for set-theoretic complementation, and further investigation into subquandle lattice complementation. She presented her work as a poster at the 2023 Joint Math Meetings, and as talks at the January 2023 Nebraska Conference for Undergraduate Women in Math and at Occidental in February 2023. Meghan also wrote a paper and gave a talk at Occidental in March 2023 for her honors project in algebraic topology with Professor Lawrence, “The Fundamental Group and Van Kampen Theorem.” After graduation, Meghan will begin the math M.S. program at Wake Forest University, and she plans to pursue a PhD in math in the future.

#### 2021

The 2021 Benedict Freedman Prize for Mathematical Promise was awarded to **IZZY THOMAS**, a math major. In his awarded research, Izzy analyzed the stream function derived in Darren Crowdy’s “Stuart vortices on a sphere” for use in magnetohydrodynamics (MHD) simulations of an active galactic nucleus (AGN). He constructed visualizations of the stream function with Python programming, provided a detailed analysis of physical parameters in the stream function and identified a velocity field derived from the stream function.

#### 2020

The 2020 Benedict Freedman Prize for Mathematical Promise was shared by **BEN C. PAGANO and ANDREA G. STINE**.** **

Ben Pagano is a math major with a double minor in theater and computer science. In the summer of 2018, he worked with Professor Naimi to construct directed graphs with intrinsic knots and links of arbitrary complexity. The following summer, he worked with Professor Sundberg and fellow student Kate Grossmann to characterize extremal hypergraphs for the Erdős-Selfridge Theorem. Finally, in the summer of 2020, through a remote REU hosted by Georgia Tech, he worked with Professor Kuzbary and fellow students to try and prove that the string link concordance group is not solvable.

Andrea Stine is currently a graduate student in mathematics at the University of California - Riverside (where she has found not only does she love doing math, she loves teaching it as well!). She graduated from Occidental with a degree in mathematics in Spring 2020 after transferring to Occidental from Missouri State University. Andrea worked with Jay Daigle in the summer of 2018 on numerical monoids, and in particular, on delta sets.

#### 2019

The 2019 Benedict Freedman Prize for Mathematical Promise was awarded to **VENA A. ZHANG**, a double major in mathematics and computer science. She conducted research on factorization theory in numerical monoids, and analyzed how adding non-irreducible elements to the set of factors affects an invariant known as the delta set. This research combined combinatorial and number-theoretic and computer simulations to understand the algebraic structure of numerical monoids. Vena also excelled in her studies, and is the recipient of the Benedict Freedman Senior Prize in Mathematics.

#### 2017

The 2017 Benedict Freedman Prize for Mathematical Promise was awarded to **THAYER A. FISHER**, a Mathematics/Chinese double major with a minor in Computer Science. He aced all his math classes with a knack for creative problem solving. Thayer did summer research on "Phylogenetic topographer: systematic exploration of the phylogenetic likelihood surface" at the Fred Hutchinson Cancer Research Center in Seattle in 2016 which led to his honor project taken with Professor Lengyel. His research combined probability theory, statistical theory, biological modeling, and sophisticated computer science techniques and applications. Thayer was twice the highest scoring Oxy student taking the Putnam competition. Fisher is also the co-recipient of the Benedict Freedman Senior Prize in Mathematics.