Mathematics Department

University of Texas at Austin

matias.delgadino at math.utexas.edu

I have always wanted to understand the world around me, and the tool I have chosen is applied mathematics.

I did my undergraduate studies at the Universidad Nacional de Córdoba (Argentina), and then went to the University of Maryland (United States) to do my Ph.D. in Applied Mathematics under the supervision of Antoine Mellet.

After my Ph.D., I held postdoctoral positions at UNESCO's ICTP (Italy) under the supervision of Francesco Maggi and Imperial College (United Kingdom) under the supervision of Greg Pavliotis and Jose Carrillo.

My research interests are mostly related to mathematical modelling through Partial Differential Equations (PDEs). For the most part, my work is devoted to understanding self-organization phenomena in systems with a large number of particles/agents. Using this perspective, I am currently trying to understand the dynamics of parameter training in commonly used machine learning algorithms.

Currently, my research is being funded by NSF DMS 2205937 and NSF RTG 1840314. In the past, my research was funded by CNPq and Instituto Serrapilheira.

- GAN: Dynamicsa for Wassertein GAN
- Oscillatory behavior for Wassertein GAN
- Interview for TV PUC-Rio
- Mixing and Enhanced dissipation Analysis seminar at University of Bath (2019)
- Mean ﬁeld limit by Gamma convergence part of the Junior trimester program in Kinetic theory at the Haussdorf Center (2019)

- Main Organizer of NSF RTG: Winter Program in Machine Learning 2024
- Main Organizer of ICTP 1st Latin American School in Applied Mathematics:
Yo soy eLLAMA

- Hearing the Self: a Spectral Experience. An interactive, audio/visual installation simulates the process by which the human brain perceives the world. Xuhui Art Museum, Shanghai (ICMC-2017)

- GAN: Dynamics at Algorithms and Analysis UT & TXST and VAPS seminar (2024)
- On the relationship between the thin film equation and Tanner's law at PDE Seminar Georgia Tech (2019) and Rio Summer PDE (2020)
- Mixing and Enhanced Dissipation at Colloquio Brasilero de Matematica IMPA (2019) and Fluid Mechanics Seminar Imperial College (2018)
- Alexandrov’s Theorem revisited at CoV and GMT University of Sussex (2018) and KCL/UCL Geometry Seminar King's College London (2018)

- Uniqueness and non-uniqueness of steady states of aggregation-diffusion equation with X. Yan and Y. Yao, Communications of Pure and Applied Mathematics (2020)
- A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles with J. Carrillo and G. Pavliotis, Journal of Functional Analysis (2020)
- On the relationship between the thin film equation and Tanner's law with A. Mellet, Communications of Pure and Applied Mathematics (2020)
- Reverse Hardy-Littlewood-Sobolev inequalities with J. Carrillo, J. Dolbeault, R. Frank and F. Hoffmann, Journal de Mathématiques Pures et Appliquées (2019)
- On the relation betweenenhanced dissipation time-scales and mixing rates with M. Coti Zelati and T. Elgindi, Communications of Pure and Applied Mathematics (2019)
- Existence of ground states for aggregation-diffusion equations with J. Carrillo and F. Patacchini, Analysis and Applications (2019)
- Alexandrov Theorem revisited with F. Maggi, Analysis & PDE (2019)
- 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 (2018)
- Hölder estimates for fractional parabolic equations with critical divergence free drifts with S. Smith, Annales de l'Institut Henri Poincaré C, Analyse non linéaire (2018)
- Convergence of the one-dimensional Cahn-Hilliard equation with degenerate mobility, SIAM Journal on Mathematical Analysis (2018)
- Regularity of local minimizers ofthe interaction energy via obstacle problems with J. Carrillo and A. Mellet, Communications in Mathematical Physics (2016)