Couplings of sub-Riemannian diffusions have attracted interest in recent years. Unlike in the Riemannian case, Markovian couplings are not optimal, even for model spaces, such as the Heisenberg group. We describe an approach to construct non-Markovian, non-coadapted couplings for sub-Riemannian Brownian motions in sub-Riemannian manifolds with large symmetry groups. Our construction is based on global isometries of the space, giving couplings that are maximal, as well as making the construction relatively simple and uniform across different manifolds. This talk is based on joint work with Robert Neel.

Speaker Biography:  Liangbing Luo works in the intersection of probability, analysis and geometry. Her research focus on functional inequalities on both finite-dimensional and infinite-dimensional geometric spaces. She published papers in Journal of Functional Analysis, IMRN, etc. She obtained her PhD from University of Connecticut under the supervision of Prof Maria Gordina in 2022 and had postdoctoral position at Lehigh University (2022-2024). She is currently a postdoc at Queen’s University from 2024.