In October 2024, I gave a research talk at the seminar of the Tufts student SIAM chapter.

In July 2024, I gave a talk at the 2024 NDSEG Fellows Conference (New Orleans, LA) titled: Gradient flow structures using an adapted Wasserstein metric geometry.

In March of 2024, I visited my advisor in Yerevan, Armenia and gave two invited talks.

• A. I. Alikhanian National Science Laboratory (Yerevan Physics Institute). Yerevan, Armenia. March 2024. Bounding the approach to oligarchy: inequalities about inequality.
• American University of Armenia. Yerevan, Armenia. March 2024. With M. Johnson. Wealth Inequality: motivation, models, and analyses.

Over the summer of 2023, I attended the 2023 Econophysics Colloquium in Lipari, Italy and gave a talk on a recent result. The talk was titled: Bounding the approach to oligarchy in a modified yard-sale model via the differential Grönwall’s inequality.

In the spring of 2023, I completed my candidacy exam, which was a lecture on my efforts to construct a Lyapunov functional for the yard-sale model with redistribution.

Title: Free-energy functionals for an econophysics equation

Abstract: We present ongoing research into the study of a partial integro-differential equation (PIDE) that arose from a kinetic mean-field theory description of an asset-exchange model. The system considered is the yard-sale model of stochastic binary exchanges with a redistributive taxation scheme.

We focus on deriving a functional — in this case, a map from a subset of probability measures over wealth into the reals — that is monotone under the dynamics induced by the PIDE. Standard procedures for deriving Lyapunov functionals are not applicable since the system has a non-local diffusion coefficient. We dwell on a particular possible form of a Lyapunov functional that is inspired naturally by considering gradient flows in 2-Wasserstein space.

The successful derivation of a Lyapunov functional could allow for new insights into the equilibrium state of the system as well as its stability and rate of convergence to equilibrium. Further, if successful, the approach may generalize to a broader class of McKean-Vlasov Fokker-Planck equations that appear in other mean-field theories.