Gabriel Rioux

Rioux Thumbnail

Email: ger84 "at" cornell "dot" edu

Office: 657 Frank H. T. Rhodes Hall

About Me

I am a fourth-year Ph.D. candidate at Cornell University's Center for Applied Mathematics working under the supervision of Ziv Goldfeld. Previously, I studied at McGill University, earning a B.Sc. in honors Mathematics and Physics in 2019 and a M.Sc. in Mathematics and Statistics in 2020 under the supervision of Prof. Rustum Choksi and Prof. Tim Hoheisel. The subject of my Master's thesis was applying the maximum entropy on the mean method to the problem of image deblurring.

Research Interests

My research interests lie broadly in optimization, mathematical statistics, and probability. I am particularly interested in the interplay between these subjects, and hence, have recently been working on problems in optimal transportation.

My most recent work has focused on studying statistical and computational aspects of the Gromov-Wasserstein distance, which is a figure of merit for comparing the inner structure of metric measure spaces. Indeed, it defines a metric on the space of metric measure spaces modulo isometries.

Its definition is akin to the standard optimal transport problem with the important distinction that the underlying objective is non-convex in general (as opposed to the linear optimal transport problem). As such, principled analysis of the Gromov-Wasserstein distance requires new techniques, and many standard results from optimal transport (e.g. duality and existence of transport maps) do not yet have a direct analogue.

Publications and Working Papers


Awards and Fellowships