Assistant professor in Mathematics at University of South Carolina.
Colloquia and RTG data science seminars.
Optimal transport and Mean field games workshop series
Draft "Geometric calculations on density manifolds from reciprocal relations in hydrodynamics" is online.
Hydrodynamics are systems of equations describing the evolution of macroscopic states in non-equilibrium thermodynamics. From generalized Onsager reciprocal relationships, one can formulate a class of hydrodynamics as gradient flows of free energies. In recent years, Onsager gradient flows have been widely investigated in optimal transport-type metric spaces with nonlinear mobilities, namely hydrodynamical density manifolds. This paper studies geometric calculations in these hydrodynamical density manifolds. We first formulate Levi-Civita connections, gradient, Hessian, and parallel transport, and then derive Riemannian and sectional curvatures on density manifolds. We last present closed formulas for sectional curvatures of density manifolds in one dimensional spaces, in which the sign of curvatures is characterized by the convexities of mobilities. In examples, we present density manifolds and their sectional curvatures in zero range models, such as independent particles, simple exclusion processes, and Kipnis-Marchioro-Presutti models.
Jan 27, 2025. 
Applied mathematics; Transport information geometry in PDEs, Data science, Graphs and Neural networks, Complex Dynamical systems, Computation, Statistics, Control and Games.
