Research
My reserach bridges several fields of mathematics: analysis, probability, and geometry. Presently, I am interested in studying the heat kernel on manifolds or graphs which can be decomposed (in some fashion) into "nice" smaller pieces. Considering heat kernel estimates often brings up interesting questions about harmonic functions, recurrence/transience, and hitting probabilities. Many of the tools I use are based on functional inequalities and probabilistic ideas.
I enjoy using techniques from a variety of different fields and am interested in thinking about mathematical objects from several different perspectives in order to gain a more complete understanding of them.
Papers and Preprints
Hitting probabilities and uniformly S-transient subgraphs (with L. Saloff-Coste), Electronic Journal of Probability, Volume 29 (2024). (link)
Heat Kernel Estimates on Manifolds with Ends with Mixed Boundary Condition (with L. Saloff-Coste). Under Revision. arXiv: 2108.05790 (2021).
Generalized Catalan Numbers and Objects: X,Y Equivalence Classes and Polyominoes (with H. Pieper). Electronic Proceedings of Undergraduate Math Day, Volume 5 (2018). (link)
Talk Slides & Videos
Heat Kernel Estimates on Manifolds with Ends with Mixed Boundary Condition
20 minute video (from the 17th Prairie analysis seminar) & Slides (20 minute version & 1 hour version)
Poster given at the 2022 AWM (Association for Women in Mathematics) Research Symposium.
(Click here for a higher quality version.)
Other Writings
Several courses I have taken required written projects. Below I've included a selection of these that others may find useful or interesting.
This paper served as my final project for MATH 7270: Topics in Numberical Analysis, taught by Alex Townsend (Spring 2019), at Cornell.
This paper served as my final project for MATH 6120: Complex Analysis, taught by Robert Strichartz (Spring 2019) at Cornell.