Status:
Personal website:
ORCID iD:
https://orcid.org/0000-0002-6897-1060
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
I have always wanted to understand the world around me, and the tool I have chosen is applied mathematics.
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.
Further details:
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.
Prizes, awards, and scholarships:
My research is being funded by Bolsa de produtividade of CNPq and Instituto Serrapilheira.
Major / recent publications:
- Uniqueness and non-uniqueness of steady states of aggregation-diffusion equation with X. Yan and Y. Yao, to appear in 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 to appear in Communications of Pure and Applied Mathematics (2019)
- 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)