Research

Broadly speaking, I research the analysis of partial differential equations, optimal transport, and calculus of variations. I am also interested in variational mean field games that incorporates optimal transport. Additionally, I study  kinetic equations.  Furthermore, some of my work is in the interface of machine learning with optimal transport.

Journal publications and preprints

• A Minimax Bilinear Transport Problem and Nash-Monge-Kantorovich Maps, with Edward Huynh In preparation.

• Generative Adversarial Networks: Dynamics, with Matias G. Delgadino, and Bruno B. Suassuna. arxiv.org/abs/2405.18673 (2024) Journal of Machine Learning. Publication, 26(181):1−30, 2025 

• Regularization estimates for the Landau-Coulomb Diffusion, with Maria Gualdani and Nestor Guillen, preprint arxiv.org/abs/2310.16012 . Nonlinear Analysis, Volume 251, February 2025, 113695.

• An optimal transportation principle for interacting paths and congestion*. (2022) arxiv.org/abs/2109.01946.Under review

• Presentation: An optimal transport problem with interaction effects (August 2024) (Slides) ( Video )

Talks

• Modeling & Computation Seminar ,  "An optimal transport problem with interaction effects". The University of Arizona, April, 2026

• Machine Learning Reading Seminar , "GAN: Dynamics". Texas State University,  March, 2026

• Differentials Equations and Applied Math Seminar , "On A MiniMax Bilinear Transport Problem". Texas State University, February, 2026

• Latinx Mathematical-sciences-conference-2025/(LatMath) hosted by IPAM at UCLA. "Special session in Harmonic Analysis, PDEs & Differential Geometry​". Los Angeles, CA. March 2025

•  JMM Special Session on Advances in Nonlinear Dispersive and Kinetic Equations, I.  Seattle, WA. Jan 8 - 11, 2025

•  Mathematics Teachers' Circle of Austin, " Beginning with the basics: Understanding the Natural Numbers".  Austin, Texas. December, 2024.

•   Analysis and Stochastic Analysis Seminar, "Regularization estimates of the Landau-Coulomb Diffusion." Auburn University, Alabama, November 20, 2024.

•  Analysis Seminar, Introductory Lecture**, "Hamiltonian-Jacobi equations and optimal control for irreversible processes." The University of Texas, Austin, September 23, 2024.

• AMS Sectional Meeting at the University of Texas, San Antonio, Special session: Mathematical Physics and Numerical Methods. San Antonio, September 14-15, 2024.​

•   BIRS workshop 24w5198,  CMO. “Optimal Transport and Dynamics”. Oaxaca, Mexico, August 2024. Talk Video 

•  Analysis and PDE seminar, "Smoothing estimates on the Landau-Coulomb diffusion".  Michigan State University, East Lansing, March 13, 2024.

•  Analysis Seminar,  Introductory Lecture** , "An optimal transport framework for Benamou-Brenier fluid mechanics theory." The University of Texas, Austin, November 13, 2023.

•   PDE and Applied Math Seminar, "Smoothing estimates for a nonlocal diffusion equation." The University of California at Riverside, October 11, 2023.

• Analysis Seminar, "An optimal transportation principle for interacting paths." The University of Texas, Austin, September 14, 2022.

As graduate student:

•  Applied Math and Computation Seminar, "Optimal transportation with interacting paths.", The University of Massachusetts, Amherst, February 15, 2022.

•  2020 CMS Winter Meeting; Optimal transport and Applications ​2020 CMS Winter Meeting (2020).

• Geometric and Harmonic Analysis, 2019 UConn, Storrs​ Geometric and Harmonic Analysis Workshop (2019)