My research is on decisions under uncertainty and I work on related problems in stochastic optimal control, Markov decision processes, nonlinear partial differential equations, probability theory, mathematical finance, and financial economics.  Recently, I have been interested in modern computational approaches to high-dimensional stochastic optimal control and mean-field (or McKean-Vlasov) stochastic optimal control, and modern learning algorithms.

I have published in leading journals in many fields, including Mathematics, Optimal Control, Applied Mathematics,  Financial Engineering, Economics, Finance, and Business.

My recent publications in mean-field games or control are:

• Potential Mean-Field Games and Gradient Flows, (with Felix Höfer), arXiv:2408.00733, (2024), Stochastic Processes and Applications, forthcoming.
• Markov perfect equilibria in discrete finite-player and mean-field games, (with Felix Höfer and Atilla Yilmaz), arXiv: 2507.04540, (2025), SIAM Journal on Control and Optimization, forthcoming
• Learning algorithms for mean-field optimal control (with Josef Teichmann, Qinxin Yan), arXiv: 2503.17869, (2025), SIAM Numerical Analysis, forthcoming.
• Synchronization Games, (with Felix Höfer), Mathematics of Operations Research, (2025).
• Viscosity Solutions of the Eikonal Equation on the Wasserstein Space, Applied Mathematics & Optimization.90(1), (with Qinxin Yan), 90 (1), 1-16, (2024).
• Viscosity Solutions of McKean-Vlasov control on a torus, (with Qinxin Yan), SIAM Journal on Control and Optimization, 30; 62(2):903-23,(2024).
• Synchronization in a Kuramoto Mean Field Game, (with Rene Carmona and Quentin Cormier), Communications in Partial Differential Equations, 2;48(9):1214-44, (2023).

Following are my recent papers in high-dimensional computational problems in optimal control:

• Neural Optimal Stopping, (with Max Reppen and Valentin Tissot-Daguette), Mathematical Finance, 35(2), pp.441-469, (2025).
• Deep level-set method for Stefan problems, Journal of Computational Physics, (with Misha Shkolnikov and Valentin Tissot‐Daguette), 503, 1-23, (2024).