My research program focuses on analyzing the asymptotic behaviour of physical systems subject to randomness. This includes the study of PDEs in heterogeneous environments (stochastic homogenization), particle systems, and random walks. I am particularly interested in the interplay between techniques from PDEs and probability theory to analyze such models.
(with Thomas Hughes), Generalized front propagation for spatial stochastic population models, submitted.
(with Gavin Barill and Maeve Wildes), Convergence of Finite Difference Schemes for Lower Semicontinuous Viscosity Solutions, submitted.
(with Louigi Addario-Berry, Gavin Barill, and Erin Beckman), The Central Limit Theorem via Doubling of Variables, submitted.
(with Scott Armstrong and Ben Fehrman), Green function and invariant measure estimates for nondivergence form elliptic homogenization, submitted.
(with Louigi Addario-Berry and Erin Beckman), Symmetric Cooperative Motion in One Dimension, Probab. Theory Relat. Fields 188, 625–666 (2024).
(with Rustum Choksi, Irene Fonseca, and Raghav Venkatraman), Anisotropic Surface Tensions for Phase Transitions in Periodic Media, Calc Var. and PDE, 61, Article number: 107 (2022).
(with Louigi Addario-Berry and Erin Beckman), Asymmetric Cooperative Motion in One Dimension, Trans. Amer. Math. Soc. 375 (2022), 2883-2913.
(with Louigi Addario-Berry and Thomas Tendron), Barycentric Brownian Bees, to appear in Annals of App. Prob.
(with Andrej Zlatoš) Stochastic Homogenization for Reaction-Diffusion Equations, Arch. Ration. Mech. Anal. 232 (2019), no. 2, 813-871
(with Amir Alwan, Zonglin Han, Zijian Tao, and Andrej Zlatoš) Multidimensional Transition Fronts for Fisher-KPP Reactions, Nonlinearity 32 (2019), no. 3, 927-941.
(with Scott Armstrong) Optimal Quantitative Estimates in Stochastic Homogenization for Elliptic Equations in Nondivergence Form, Arch. Ration. Mech. Anal. 225 (2017), no. 2, 937–991.
(with Charles K. Smart) Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations , Analysis and PDE 8(2015), no. 6, 1497-1539.
A Quantitative Regularity Estimate for Nonnegative Supersolutions of Fully Nonlinear Uniformly Parabolic Equations, Communications in Partial Differential Equations 40 (2015), no.9, 1688-1704.
On the Stochastic Homogenization of Fully Nonlinear Uniformly Parabolic Equations in Stationary Ergodic Spatio-Temporal Media, Journal of Differential Equations 258 (2015), no. 3, 796-845.
(with Domenico Aiello, Hansheng Diao, Zhou Fan, Daniel O. King, and Cesar E. Silva) Measurable Time-Restricted Sensitivity, Nonlinearity 25 (2012) 3313-3325.
(with William Ott) Observing Infinite-Dimensional Dynamical Systems , SIAM J. Appl. Dyn. Syst. 9 (2010) pp.1229-1234.