Curriculum Vitae

NSF-funded research · Award DMS-2246491

• Formulated the Berry–Esseen framework for the unwrapped displacement and proved the overdamped results.
• Proved the main underdamped theorem and supporting propositions via a direct Markov-additive treatment of the displacement; verification of Assumption (A2) was carried out by O. Smith.
• Proved in Proposition 11.1 that, for one-dimensional periodic underdamped dynamics started from equilibrium and sufficiently small positive γ, the Berry–Esseen constant C_γ can be chosen with C_γ ≤ Cγ^−1/2, where C is independent of γ.
• Simulated overdamped and underdamped transport, measured the friction-dependent constants, and compared them with the averaged energy dynamics.

The joint manuscript also includes additional numerical analysis by A. Valse.

• Analyze bounded continuous prepayment perturbations in the Papi–Briani MBS model at p = 2 using viscosity theory and a Lipschitz BSDE representation.
• Established a bounded linear price response with a uniform second-order remainder, yielding Fréchet differentiability and mean-square sensitivity.
• Derived centered-noise mean-bias and Hilbert-space variance expansions; linked the leading price variance to the input-noise covariance.
• Planned for Spring 2027: extend the MBS evolution to an SPDE with additive noise; study well-posedness, moment bounds, stability, small-noise limits, and numerical simulation.

Past exploratory study of Haar-distributed unitary matrices and quantum expanders.