I welcome opportunities to share my mathematical knowledge and personal experiences within the field with undergraduates and more junior mathematicians, particularly those underrepresented in mathematics. I am especially excited to share the process of mathematical discovery with undergraduates through research experiences.
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. 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," which is a key step in computing the slope gap distribution, and we applied this algorithm to compute the distribution for the double heptagon translation surface. We are currently in the process of writing up these results for publication. I also organized a grad school panel and DEI reading group for participants from across the different research groups in the SUMRY program.
Senior Thesis Advising at Pomona College
Emil Adams, '24: Auction theory and the winner's curse
Nico Santamaria, '25: Judgment aggregation and opinion dynamics
Xiaoxing Yu, '25: Slope gap distributions on square-tiled surfaces
Other Mentoring Experience
Math Alliance Mentor since Fall 2024
Mentored a group of four undergraduates at UCSD in the study of ergodic theory with applications to number theory
Mentored a female undergraduate math major at UT Austin through a program organized by the UT Austin math club
Participated in UT Austin's Directed Reading Program for undergraduates