I am a probabilist at the University of Washington.

I love probability. Over the years my research covered such diverse topics such as interacting Brownian particle systems, random graphs and random matrices, stochastic portfolio theory, information geometry, and evolving random trees. My current research obsession is the Monge-Kantorovich optimal transport problem and its recent exciting applications to what can be broadly called data science. My research is currently supported partially by NSF grant DMS-2052239, DMS-2134012 (Scale Math of Deep Learning).

I work with a large number of collaborators, mathematicians of various stripes, statisticians and computer scientists. Much of this is facilitated by the Kantorovich Initiative which we convened a few years back to facilitate interdisciplinary research dedicated to the mathematics of optimal transport and its dissemination towards a wide audience of researchers, students, industry, policy makers and the general public. The Initiative is currently being funded by the first ever PIMS Research Network grant and an NSF Infrastructure grant DMS-2133244. There are a lot of activities organized by KI including regular online courses in case you are interested to learn the subject. If you are curious, check the KI webpage and sign up for the mailing list.

I am the current associate chair of the math department and the current director for the Applied and Computational Mathematical Sciences (ACMS) major at UW. ACMS is one of the most sought-after undergraduate majors in campus. I am also a current associate editor for Stochastic Models, Electronic Journal of Probability, and the Electronic Communications in Probability. In the past, I have been an associate editor for The Annals of Probability (2012--2017) and The Annals of Applied Probability (2010--2015).

If you're thinking about joining our research group, check out the slides from some of my recent talks. You may also send me a message and I will tell you all about it, although, fair warning, it can take me a while to reply. Alternatively you can ask one of my wonderful ex-Ph.D. students: Tobias Johnson, Andrey Sarantsev, Ting-Kam Leonard Wong, David Clancy, and Lang Liu, or one of my current Ph.D. students Raghavendra Tripathi and Garrett Mulcahy. If you'd rather talk to one of my past or current postdocs, feel free to contact any of the following wonderful people: Noah Forman, Moumanti Poddar, Andrea Ottolini, and Nabarun Deb.

In Fall 2023 I am teaching a PIMS online graduate class on OT+ grad flow (Optimal Transport + Wasserstein gradient flow). See here for more details. This is a part of a series of online courses offered by the Kantorovich Initiative. For UW students: if you are enrolled in one of my classes, you can find the course material in Canvas.

Slides from recent work

Wasserstein mirror gradient flows

Limits of large scale network optimization

Image credit Raghav Somani.

Entropic regularization of optimal transport

Image credit Marco Cuturi.

Aldous diffusion on continuum trees

Image credit Wikipedia.

Sparse random regular graphs, eigenvalues, and dynamics

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    University of Washington, Seattle, WA
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