Research

Overview

I am interested in the effects that randomness can have on models coming from the physical and social sciences. My research is often involved at the border of rough (or stochastic) analysis and partial differential equations (PDE).

Some particular topics I'm interested in include interacting agent systems, mean field games and mean field control, rough paths, stochastic partial differential equations, and homogenization.

My research is supported by the National Science Foundation under award number DMS-2437066. The topic of the grant is "Nonlinear Stochastic Partial Differential Equations."

Publications

Mean field games with common noise and degenerate idiosyncratic noise (with P. Cardaliaguet and P. E. Souganidis), 2022. To appear in Ann. Appl. Probab. [arXiv]
Well-posedness of Hamilton-Jacobi equations in the Wasserstein space: non-convex Hamiltonians and common noise (with S. Daudin and J. Jackson), 2023. To appear in Comm. Partial Differential Equations [arXiv]
Linear and nonlinear transport equations with coordinate-wise increasing velocity fields (with P.-L. Lions), 2023. To appear in Ann. Inst. H. Poincaré Anal. Non Linéaire. [arXiv]
Transport equations and flows with one-sided Lipschitz velocity fields (with P.-L. Lions), 2023. Arch. Rational Mech. Anal. 2024
A comparison principle for semilinear Hamilton-Jacobi-Bellman equations in the Wasserstein space (with Samuel Daudin). Calc. Var. Partial Differential Equations, 2024.
The Neumann problem for fully nonlinear SPDE (with P. Gassiat), Ann. Appl. Probab., 2024
Interpolation results for pathwise Hamilton-Jacobi equations (with P.-L. Lions and P. E. Souganidis), Indiana Univ. Math. J., 2022
Besov rough path analysis (with P. Friz), J. DIfferential Equations, 2022
Dimension reduction techniques in deterministic mean field games (with J.-M. Lasry and P.-L. Lions), Comm. Partial Differential Equations, 2022
Hölder regularity of Hamilton-Jacobi equations with stochastic forcing (with P. Cardaliaguet), Trans. Amer. Math. Soc., 2021
Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations, Lect. Notes Comput. Sci. Eng., 2021
Homogenization of a stochastically forced Hamilton-Jacobi equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2021
Scaling limits and homogenization of mixing Hamilton-Jacobi equations, Comm. Partial Differential Equations, 2021
Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations, Ann. Appl. Probab., 2020
Perron's method for pathwise viscosity solutions, Comm. Partial Differential Equations, 2018
Homogenization of pathwise Hamilton-Jacobi equations, J. Math. Pures Appl., 2018
On the size of the resonant set for the products of 2x2 matrices, Involve, 2011

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