Research Group
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Overview
My research area is in mathematical physics, analysis, and probability.
My current projects involve the study of the discrete approximation of quantum systems, scaling limits and invariance principles in probability, the properties of path measures, distributions, and measures on real and non-Archimedean spacetimes that respect certain symmetries, and the extent to which compositionality determines the analytical features of models for physical systems.
I am also interested in research in mathematics education. Please see my teaching page for more information on this area.
Zuma "the Bear" Weisbart enjoys checking over estimates. Although he has not yet earned his PhD, he has acknowledgements in two dissertations for his valuable assistance!
Current Projects
The discrete approximation of non-Archimedean diffusion processes.
Path integrals in probability and quantum theory.
The properties of diffusion processes that respect symmetries associated with the state spaces.
Development of stochastic methods for investigating discrete and finite approximations of quantum systems.
The use of distributions for classifying elementary particles, and the relationship between symmetries of distributions and their growth and smoothness properties.
The development of categorical tools for providing a compositional framework in which to study physics (currently classical mechanics).
This page will be continuously updated. My work is interdisciplinary, and I am always open to new projects and new directions.
Last update: 8/12/2025
Current and Former Ph.D. Students
Important Notification
My graduate students and former graduate students are very bright, strong mathematicians, great teachers, and terrific people. If you have any positions available, you should write to them and offer them a job as soon as possible. You will not be disappointed!
Former Ph.D. Students
Dr. Rahul Rajkumar
Dr. Rahul Rajkumar
Rahul 'Raj' Rajkumar was awarded his doctorate in Summer, 2025.
Raj will soon begin his postdoc at the Institute of Mathematics in Academia Sinica, in Taipei, Taiwan, under the supervision of Colin McSwiggen.
Raj's PhD research focused on the path properties of stochastic processes valued in non-Archimedean local fields, such as the p-adic numbers, and related spaces. A counterpart to the real-valued setting, processes in these exotic spaces challenge intuition and provide insight into the essential nature of the classical objects. Rahul is excited by problems from pure, applied, and industrial mathematics - studying probability theory enables him to explore these diverse interests.
Rahul was supported by the UC Riverside Chancellor's Distinguished Fellowship Award, and was the M.M. Rao Award recipient for 2023-2024.
When not teaching or mentoring undergraduate students, Rahul played bassoon with the UC Riverside Wind Ensemble, and was the treasurer of the local AMS Graduate Student Chapter.
Dr. Tyler Pierce
Dr. Tyler Pierce
Tyler Pierce was awarded his doctorate in Summer, 2024.
Hi, my name is Tyler Pierce and I am currently an assistant Professor of Mathematics and Statistics at Cosumnes River College, in Sacramento. I work with Dr. David Weisbart on diffusion processes. I am particularly interested in two things, applications of diffusion processes and math education.
Outside of math I enjoy going to the gym, cycling, drumming, traveling, listening to music, and hanging out with my dog Stout.
Dr. Adam Yassine
Adam Yassine was awarded his doctorate in Spring, 2020.
I am from Pomona and have lived in Southern California for most of my life. In summer, 2019, I was a teaching assistant at UC Riverside for a Faculty Led Education Abroad Program (FLEAP) in probability theory, which was taught at University College London (UCL). After the course, my collaborators and I continued working with undergraduates who participated in the FLEAP program on a research project that led to a publication. After finishing my PhD, I spent one year as a tenure-track Assistant Professor at The American University in Cairo, and two years as a postdoc at Bowdoin College. I am currently a postdoc at Pomona College.
I am very passionate about outreach and mentorship. I am directing an undergraduate summer research project studying the statistical mechanics of spin glasses.
In addition, I am an instructor for the Pomona College Academy for Youth Success (PAYS) program, which seeks to support local high school students by preparing them for admission to selective colleges and universities.
I am also an avid math book collector!
Current Ph.D. Students
Andrea Abeje-Stine
Andrea Abeje-Stine
Hi! I'm Andrea. My primary research project involves developing a compositional framework for classical mechanical systems using category theoretic tools. I also work with Dave's other advisees in determining scaling limits of Brownian motion in non-Archimedean spaces.
In Summer 2023, I completed a trading internship at Belvedere Trading, where I learned about options market making and developed tools in Python to assist real-time trading decisions. In Summer 2024, I completed an internship at Peak6 Capital Management.
I've also been learning about how state space machine learning models like Mamba might be used for efficiently understanding time series data. You can find more information about me at andreagstine.com.
Alex Cohen
Alex Cohen
Hi, my name is Alex Cohen and I am currently a 4th year Ph.D. student at UC Riverside. I work on the spectral theory and the finite approximation of quantum systems.
I am interested in the application of functional integration in operator theory. A side interest of mine is to bring categorical tool to the study of analysis and probability.
Outside of math, I enjoy studying history and philosophy. I especially enjoy reading the works of Joseph Campbell.
David Kissee
David Kissee
© Copyright 2023 by David Weisbart.All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from David Weisbart.
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