Matias G. Delgadino

Matias Gonzalo Delgadino


Assistant Professor
Department of Mathematics
The University of Texas at Austin
matias.delgadino at math.utexas.edu

Short Bio

My research focuses on the mathematical analysis of complex systems. Whether I study the dynamics of fluids, the aggregate behavior of interacting particles, or the sampling algorithms that power modern artificial intelligence, these diverse phenomena can often be described through a common mathematical language: partial differential equations (PDEs)—equations that connect change in time with variation in space.

Rather than relying on empirical success alone—for example, an AI model that appears to work in practice—I study why a method works, when it fails, and what guarantees can be proved. To do this, I combine tools from optimization theory (the calculus of variations) and the mathematics of randomness (stochastic analysis) to uncover the core structures that drive these systems.

  • Research Funding: Supported by the National Science Foundation under grant NSF DMS 2205937 (2022–2026).
  • Past Appointments: Hooke Research Fellow at the University of Oxford; Assistant Professor at PUC-Rio (Brazil); Postdoctoral Researcher at Imperial College London (UK) and UNESCO's ICTP (Italy).
  • Education: Ph.D. in Mathematics from the University of Maryland, College Park; Licenciatura en Matematica from the Universidad Nacional de Córdoba (Argentina).

Publications

Preprints and Work Under Review
  1. Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance with F.U. Caja-Lopez and J. Kitagawa, 2026.
  2. Mass generation for the two-dimensional O(N) linear sigma model in the large N limit with S.A. Smith, 2026.
  3. Diffusion-based posterior sampling: a Feynman--Kac analysis of bias and stability with S. Motsch, A. Parulekar, W. Porteous, and S. Shakkottai, 2026.
  4. Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on S² with L. Melzi, 2025.
  5. Sharp mean-field estimates for the repulsive log gas in any dimension with R.S. Gvalani, 2025.
  6. Contractivity of Wasserstein distance and exponential decay for the Landau equation with Maxwellian molecules with F.U. Caja-Lopez, M.P. Gualdani, and M. Taskovic, 2025.
Published and Accepted Papers
  1. Entropy maximization in the two-dimensional Euler equations with M. Coti Zelati, Analysis & PDE 19(3), 505--538, 2026. DOI
  2. Continuous symmetrizations and uniqueness of solutions to nonlocal equations with M. Vaughan, Analysis & PDE, 2025. DOI
  3. Generative adversarial networks: dynamics with B.B. Suassuna and R. Cabrera, Journal of Machine Learning Research 26(181), 1--30, 2025. JMLR
  4. The Landau equation as a gradient flow with J.A. Carrillo, L. Desvillettes, and J.S.H. Wu, Analysis & PDE 17(4), 1331--1375, 2024. DOI
  5. A Heintze--Karcher inequality with free boundaries and applications to capillarity theory with D. Weser, Journal of Functional Analysis 287(9), 110584, 2024. DOI
  6. Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions with R.S. Gvalani, G.A. Pavliotis, and S.A. Smith, Communications in Mathematical Physics 401(1), 275--323, 2023. DOI
  7. Convergence of a particle method for a regularized spatially homogeneous Landau equation with J.A. Carrillo and J.S.H. Wu, Mathematical Models and Methods in Applied Sciences 33(5), 971--1008, 2023. DOI
  8. Boltzmann to Landau from the gradient flow perspective with J.A. Carrillo and J.S.H. Wu, Nonlinear Analysis 219, 112824, 2022. DOI
  9. Fast diffusion leads to partial mass concentration in Keller--Segel type stationary solutions with J.A. Carrillo, R.L. Frank, and M. Lewin, Mathematical Models and Methods in Applied Sciences 32(4), 831--850, 2022. DOI
  10. Uniqueness and nonuniqueness of steady states of aggregation-diffusion equations with X. Yan and Y. Yao, Communications on Pure and Applied Mathematics 75(1), 3--59, 2022. DOI
  11. On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions with R.S. Gvalani and G.A. Pavliotis, Archive for Rational Mechanics and Analysis 241(1), 91--148, 2021. DOI
  12. On the relationship between the thin film equation and Tanner's law with A. Mellet, Communications on Pure and Applied Mathematics 74(3), 507--543, 2021. DOI
  13. A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles with J.A. Carrillo and G.A. Pavliotis, Journal of Functional Analysis 279(10), 108734, 2020. DOI
  14. On the relation between enhanced dissipation time-scales and mixing rates with M. Coti Zelati and T.M. Elgindi, Communications on Pure and Applied Mathematics 73(6), 1205--1244, 2020. DOI
  15. Reverse Hardy--Littlewood--Sobolev inequalities with J.A. Carrillo, J. Dolbeault, R.L. Frank, and F. Hoffmann, Journal de Mathématiques Pures et Appliquées 132, 133--165, 2019. DOI
  16. Existence of ground states for aggregation-diffusion equations with J.A. Carrillo and F.S. Patacchini, Analysis and Applications 17(3), 393--423, 2019. DOI
  17. Alexandrov's theorem revisited with F. Maggi, Analysis & PDE 12(6), 1613--1642, 2019. DOI
  18. Convergence of a one-dimensional Cahn--Hilliard equation with degenerate mobility, SIAM Journal on Mathematical Analysis 50(4), 4457--4482, 2018. DOI
  19. Hölder estimates for fractional parabolic equations with critical divergence free drifts with S.A. Smith, Annales de l'Institut Henri Poincaré C 35(3), 577--604, 2018. DOI
  20. Bubbling with L²-almost constant mean curvature and an Alexandrov-type theorem for crystals with F. Maggi, C. Mihaila, and R. Neumayer, Archive for Rational Mechanics and Analysis 230(3), 1131--1177, 2018. DOI
  21. Regularity of local minimizers of the interaction energy via obstacle problems with J.A. Carrillo and A. Mellet, Communications in Mathematical Physics 343(3), 747--781, 2016. DOI
Interdisciplinary Work

Mentoring

Current Ph.D. Students Graduated Ph.D. Students
  • Jeremy Wu (University of Oxford, 2018–2022, co-advised with J.A. Carrillo) — now Assistant Professor at the University of Manitoba
  • Daniel Weser (UT Austin, 2020–2022, co-advised with F. Maggi) — now Postdoc at UNC Chapel Hill
  • Kenneth DeMason (UT Austin, 2021–2025), NSF Graduate Research Fellow — now Postdoc at McMaster University
Postdocs
  • Mary Vaughan (UT Austin, 2021–2023) — now Assistant Professor at Texas State University
  • Rene Cabrera (UT Austin, 2022–2025) — now Instructor at UT Austin
Undergraduates
  • Reese Feldmeier (UT Austin, 2022–2024) — now Ph.D. student in Statistics at Stanford University
  • Bruno Suassuna (PUC-Rio) — now Ph.D. student at PUC-Rio
  • Humberto Seghetto (PUC-Rio) — now Ph.D. student at PUC-Rio

Selected Slides

Videos

Outreach & Organization