Mentoring

Senior Thesis Advising at Pomona College

• Taylor Campbell, '26: An algorithm for predicting knitted gauge

• Aaron Christopherson, '26: Iterated function systems and fractal geometry

• Matthew Eichner, '26: An integer sequence derived from reduced Cantor set endpoint numerators

• Nico Santamaria, '25: Judgment aggregation in social networks: A model of deliberative democracy

• Xiaoxing Yu, '25: Origami slope gaps and the Hall distribution

• Emil Adams, '24: Auction theory and the winner's curse

SUMRY 2020

In 2020, I co-mentored, along with Caglar Uyanik, a group of three Yale undergraduates on a research project in the area of slope gap distributions on translation surfaces as part of the Summer Undergraduate Research at Yale (SUMRY) program. We computed the slope gap distributions for the family of translation surfaces arising from the regular 2n-gons with opposite sides glued, resulting in a peer-reviewed publication. We found linear upper- and lower-bounds on the number of points of non-analyticity in the distributions, providing the first example of a family of translation surface with unbounded number of points of non-analyticity. Our calculations also provided the first examples of slope gap distributions which are not unimodal. In addition to mathematical mentoring, Caglar and I also helped the students learn how to effectively communicate mathematics through writing and oral presentations, and how to navigate academic publishing and peer-review.

SUMRY 2021

Starting in 2021, the SUMRY program received an NSF grant to extend its reach by including students from outside of Yale. In 2021 I mentored a group of four undergraduates from various institutions on another project on slope gap distributions. We worked on computing the distribution for a particular square-tiled surface and developed new computational tools for investigating the distributions of square-tiled surfaces, and work for this project is ongoing. I also helped my students prepare and deliver a talk at the REU Vir(tu)al Conference 2021, and I helped organize program-wide events for the SUMRY program, such as a DEI reading group and grad school panel.

SUMRY 2023

In 2023, I co-mentored a group of five undergraduates from different institutions with with Fernando Al Assal on another project related to slope gap distributions. We developed an algorithm for streamlining the process of finding so-called "winning vectors" for a Veech surface. This key step in calculating the slope gap distribution had previously been an ad hoc part of the process, unique to each surface studied. We then applied this algorithm to compute the distribution for the regular double heptagon translation surface, and our results are now available on the arXiv. I also organized a grad school panel and DEI reading group for participants from across the different research groups in the SUMRY program.