Overview
My research is primarily in the area of stochastic partial differential equations (SPDE). Some specific topics of recent interest:
- SPDE in "critical" (scale-invariant) and "super-critical" (high-dimensional) settings.
- Ergodic theory of the stochastic Burgers equation.
Current Appointments & Affiliations
Assistant Professor of Mathematics
·
2023 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Jointly stationary solutions of periodic Burgers flow
Journal Article Journal of Functional Analysis · December 15, 2024 For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled invariant measures an ... Full text CiteSimultaneous global inviscid Burgers flows with periodic Poisson forcing
Preprint · June 11, 2024 Full text CiteViscous shock fluctuations in KPZ
Preprint · June 10, 2024 Full text CiteRecent Grants
Stochastic partial differential equations: the critical dimension and invariant measures
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2024 - 2027View All Grants
Education, Training & Certifications
Stanford University ·
2020
Ph.D.