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
UNIQUENESS AND ROOT-LIPSCHITZ REGULARITY FOR A DEGENERATE HEAT EQUATION
Journal Article SIAM Journal on Mathematical Analysis · January 1, 2025 We consider nonnegative solutions of the quasilinear heat equation in one dimension. Our solutions may vanish and may be unbounded. The equation is then degenerate, and weak solutions are generally nonunique. We introduce a notion of strong solution that e ... Full text CiteJointly 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 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.