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Research

My research interests are optimal transport, calculus of variations, and partial differential equations. In particular, I am interested in fluid mechanics and gradient flow results for problems in applied optimal transport. Recently, I've been interested in variational mean field games theory associated only with optimal transport, and kinetic equations like the Vlasov-Poisson equations.​
Preprints & Publications
​
  • Generative Adversarial Networks: Dynamics, with Matias G. Delgadino , and Bruno B. Suassuna. arxiv.org/abs/2405.18673 (2024) submitted​
  •  Regularization estimates for the Landau-Coulomb Diffusion, with Maria Gualdani and Nestor Guillen, preprint arxiv.org/abs/2310.16012 ​ (2024).  Nonlinear Analysis, Volume 251, February 2025, 113695.
  • ​An optimal transportation principle for interacting paths and congestion* .(2022) arxiv.org/abs/2109.01946   Under review

Invited talks /workshops/conferences

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

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

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

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

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

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

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

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

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

As graduate student:

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

2. 2020 CMS Winter Meeting; Optimal transport and Applications
​https://www2.cms.math.ca/Events/winter20/abs/ota#rc

1. Geometric and Harmonic Analysis, 2019 UConn, Storrs
​https://gaha2019.math.uconn.edu/









** In this preparatory talk, I introduced some key concepts and provided context in preparation for guest speakers technical seminar talk; geared towards graduate students.
* this preprint is based on my dissertation at UMASS
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