Matias G. Delgadino
Matias Gonzalo Delgadino

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

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Short Bio

I am an Assistant Professor of Mathematics working on the mathematical analysis of complex systems. Whether in the dynamics of fluids, the collective behavior of interacting particles, or the sampling algorithms behind modern generative AI, these phenomena share a common mathematical language: partial differential equations (PDEs). Combining tools from the calculus of variations and stochastic analysis, I study why these systems behave the way they do — from sharp mean-field estimates for singular interacting particle systems to the dynamics, stability, and bias of generative algorithms such as GANs and diffusion models.

  • Research Funding: Supported by the National Science Foundation under grant NSF DMS 2205937.
  • Mentoring: I have advised seven Ph.D. students (three graduated), mentored two postdoctoral researchers, and supervised several undergraduates at UT Austin and earlier at PUC-Rio and Oxford. Former mentees now hold faculty positions (Manitoba, Texas State) and postdoctoral positions (UNC, McMaster).
  • 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).

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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, 2026.
  2. Continuous symmetrizations and uniqueness of solutions to nonlocal equations with M. Vaughan, Analysis & PDE, 2025.
  3. Generative adversarial networks: dynamics with B.B. Suassuna and R. Cabrera, Journal of Machine Learning Research 26(181), 1--30, 2025.
  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.
  5. A Heintze--Karcher inequality with free boundaries and applications to capillarity theory with D. Weser, Journal of Functional Analysis 287(9), 110584, 2024.
  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.
  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.
  8. Boltzmann to Landau from the gradient flow perspective with J.A. Carrillo and J.S.H. Wu, Nonlinear Analysis 219, 112824, 2022.
  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.
  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.
  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.
  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.
  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.
  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.
  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.
  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.
  17. Alexandrov's theorem revisited with F. Maggi, Analysis & PDE 12(6), 1613--1642, 2019.
  18. Convergence of a one-dimensional Cahn--Hilliard equation with degenerate mobility, SIAM Journal on Mathematical Analysis 50(4), 4457--4482, 2018.
  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.
  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.
  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.
Interdisciplinary Work