I am a 5-th year Ph.D. Candidate in Mathematics under Professor David Weisbart at UC Riverside.
I am broadly interested in problems in Probability Theory and Stochastic Processes.
In my graduate work I study analogues of Brownian motion valued in p-adic fields and their symmetries.
I obtained my B.A. in Mathematics at NYU in 2020.
My CV
I am a classically trained saxophonist. I am currently the bassoonist for the UC Riverside Wind Ensemble.
Diversity, Equity, & Inclusion
I believe that mathematics is one of humanity’s great achievements, comparable to the study of great literature from the world over. As such, no one should be excluded from learning about mathematics. I support DEI organizations including Spectra: The Association for LGBT Mathematicians and AWM: The Association for Women in Mathematics.
Research
My graduate research focuses on properties of Brownian motion valued in p-adic fields as part of a general principle that all completions of the rationals should be studied on even footing. By studying p-adic Brownian motion, we separate properties that are intrinsic to Brownian motion from those that are due to the classical setting. For example, we show that multidimensional Brownian motion is not in general equivalent to multiple independent Brownian motions in the coordinate axes [Journal of Fourier Analysis and Applications]
I go into more detail about my ongoing projects in my Research Statement. However, some key excerpts are:
- Understanding the effects of configuration space symmetries on Brownian motion
- Determining Levy Forgery and Onsager-Machlup type results in p-adic settings
- Understanding the p-adic Coulomb problem as posed by Varadarajan
In addition to this main program, I am interested in studying Probability and Stochastic Processes more broadly. Some future directions in Probability that I would like to explore include
- Random Matrix Theory
- Random Walks on Groups
- Applications, including to Operations Research