• I am a second-year PhD student in the Department of Mathematics at University of Connecticut, Storrs. My advisor is Dr. Masha Gordina.

My research interests are in the intersection of analysis, probability and geometry. I am currently interested in Stochastic analysis on Wasserstein space: one can formally view the Wasserstein space of probability measures over Euclidean space as a Riemannian manifold. This is an inexact analogy in many severe ways - for example, what are the coordinate charts? But at the same time, one can use familiar objects from the Riemannian setting, such as tangent spaces and geodesics, to answer tricky questions. 

For probability, a central object on Riemannian manifolds is Brownian motion, which can be defined in many equivalent ways - for ex., its analytical properties (the generator) or probabilistic properties (transition kernel). I am currently thinking about how we can develop this object on the Wasserstein space.

I am also interested in Wasserstein geometry-informed algorithms for variational inference. 

• I used to be an undergraduate student at Johns Hopkins University, where I double-majored in AMS & Mathematics. I graduated in May 2024.

• My email is shu24001@uconn.edu. Here is my most recent curriculum vitae.