My research interests intersect probability, geometry, and analysis. More particularly, they include infinite-dimensional analysis, Gaussian measures and processes, stochastic differential equations on Lie groups (and sometimes more general manifolds), Markov processes and semigroups, differential operators and hypoellipticity theory. My articles on arXiv.

• Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise with F. Baudoin, M. Gordina, D. Herzog, and J. Kim
  arXiv: 2311.01440, 2023.

• Large deviations principle for sub-Riemannian random walks with M. Gordina and J. Wang
  arXiv: 2210.05817, 2022.

• Quasi-invariance for infinite-dimensional Kolmogorov diffusions with F. Baudoin and M. Gordina
  Potential Analysis, 2023.

• Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
  Journal of the Mathematical Society of Japan, 73, 1159-1185, 2021.

• Small-time asymptotics for subelliptic Hermite functions on SU(2) and the CR sphere with J. Campbell
  Potential Analysis, 53, 1063–1095, 2020.

• Convergence rates of the empirical spectral measure of unitary Brownian motion with E. Meckes
  Annales Henri Lebesgue, 1, 247-265, 2018.

• Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups with B. Driver and N. Eldredge
  Transactions of the AMS, 368, 989-1022, 2016.

• Small deviations for time-changed Brownian motions and applications to second-order chaos with D. Dobbs
  Electronic Journal of Probability, 19, 1-23, 2014.

• Smoothness of heat kernel measures on infinite-dimensional Heisenberg-like groups with D. Dobbs
  Journal of Functional Analysis, 264, 2206-2223, 2013.

• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups with F. Baudoin and M. Gordina
  Transactions of the AMS, 365, 4313-4350, 2013.

• A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups with M. Gordina
  Probability Theory and Related Fields, 155, 379-426, 2013.

• Heat kernel analysis on semi-infinite Lie groups
  Journal of Functional Analysis, 257, 3552-3592, 2009.

• Malliavin calculus for Lie group-valued Wiener functions with note
  Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12, 67-89, 2009.

• Hypoelliptic heat kernel inequalities on Lie groups
  Stochastic Processes and their Applications, 118, 368-388, 2008.

• Hypoelliptic heat kernel inequalities on the Heisenberg group with B. Driver
  Journal of Functional Analysis, 221, 340-365, 2005.