Diego González Sánchez
Postdoctoral researcher
Alfréd Rényi Institute of Mathematics

I am a postdoctoral researcher at the Álfred Rényi Institute of Mathematics in Budapest working with Balázs Szegedy. My research interests include additive combinatorics and its relations with ergodic theory, probability and dynamical systems. I am also interested in the theory of convergence and generalization of deep neural networks.

Research

Publications

1. On measure-preserving F_p^\omega systems of order k, (with P. Candela and B. Szegedy), Accepted for publication at Journal d'Analyse Mathèmatique arXiv link.
2. On higher-order Fourier analysis in characteristic p (with P. Candela and B. Szegedy). Ergodic Theory and Dynamical Systems, 1-70 (2023) Published version arXiv link.
3. A refinement of Cauchy–Schwarz complexity. , (with P. Candela and B. Szegedy). European Journal of Combinatorics 106, 103592 (2022) Published version arXiv link.
4. A Refinement of Cauchy- Schwarz Complexity, with Applications, (with P. Candela and B. Szegedy) Extended Abstracts EuroComb 2021, 293-298 (2021) Published version (This is a short version A refinement of Cauchy–Schwarz complexity presented at for EUROCOMB 2021).
5. Optimal transport with f-divergence regularization and generalized Sinkhorn algorithm, (with D. Terjék). International Conference on Artificial Intelligence and Statistics, 5135-5165 (2022) Published version arXiv link.
6. New estimates for exponential sums over multiplicative subgroups and intervals in prime fields, (with D. Di Benedetto, M. Z. Garaev, V. C. Garcia, I. E. Shparlinski, and C. A. Trujillo). Journal of Number Theory, Volume 215, (2020), Pages 261-274 Published version arXiv link.
7. On sets with small sumset and m-sum-free sets in Z/pZ , (with P. Candela and D. J. Grynkiewicz), Bulletin de la Société Mathématique de France, Toem 149, Fascicule 1, (2021), pp. 155-177 Published version arXiv link.
8. A step towards the 3k−4 conjecture in Z/pZ and an application to m-sum-free sets, (with P. Candela and D. J. Grynkiewicz), Acta Mathematica Universitatis Comenianae, Volume 88, (2019), Issue 3, pp. 521-525, Published version (This is a short version of On sets with small sumset and m-sum-free sets in Z/pZ presented at EUROCOMB 2019).
9. A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets ,(with P.-Y. Bienvenu and A. D. Martínez), Proceedings of the American Mathematical Society 148 (2020), 23-31, Published version arXiv link.
10. On nilspace systems and their morphisms, (with P. Candela and B. Szegedy), Ergodic Theory and Dynamical Systems 1-15 (2019), Published version arXiv link.
11. A Plünnecke-Ruzsa inequality in compact abelian groups.,(with P. Candela and A. de Roton), Revista Matemática Iberoamericana Volume 35, Issue 7, (2019), pp. 2169–2186, Published version arXiv link.

Preprints

1. On the inverse theorem for Gowers norms in abelian groups of bounded torsion , (with P. Candela and B. Szegedy), arXiv link.
2. Free nilspaces, double-coset nilspaces, and Gowers norms, (with P. Candela and B. Szegedy), arXiv link.
3. A framework for overparameterized learning, (with D. Terjék), arXiv link.
4. On F_2^\omega-affine-exchangeable probability measures, (with P. Candela and B. Szegedy), arXiv link.

Ph.D. thesis

1. Topics in additive combinatorics and higher order Fourier analysis Autonomous University of Madrid, PhD advisor: Pablo Candela. Extraordinary Prize of the Autonomous University of Madrid to the best PhD theses of 2019 - 2020. Published version.

Teaching

Contact

• Address

  Alfréd Rényi Institute of Mathematics
  Reáltanoda utca 13-15, 1053 Budapest, Hungary

• Email

  diegogs (at) renyi (dot) hu