Broadly, I work in stochastic analysis and control, mean-field game theory, and their applications to asset pricing and macroeconomic theory. Current directions include stochastic control under partial observability and partially observable mean-field games, with an emphasis on robustness, learning, and equilibrium behavior under model uncertainty.
◘ Stochastic Filtering and Control in Partially Observable Diffusion Models
A topic proposal exploring linear and nonlinear filtering theory with applications to partially observable stochastic control problems.
◘ C*-Algebras Generated by Weakly Quasi-Lattice Ordered Groups
Expository dissertation following Nica's framework; fills in omitted details and develops conditions for amenability via Toeplitz and universal C*-algebras.
◘ Khovanov Homology of Knots and Links
An expository write-up on categorification of the Jones polynomial and computations of Khovanov homology for simple knots.