Research interests: Functional Analysis and Operator Theory (especially dynamics of linear operators); connections with additive combinatorics, ergodic theory, and nonstandard analysis. More recently, my work explores how operator-theoretic dynamics inform the theoretical foundations of deep learning, particularly in interpolation, regularization, and structured representation learning.
Deep Learning
Y. Puig, From Attention to Orbits: Structured Learning via Shift Dynamics, submitted to NeurIPS 2025.
Y. Puig, Tree of Orbit Transformations: A Universal Topology Learner, manuscript in preparation.
Y. Puig, Orbit Regularization for Robust Structured Learning, manuscript in preparation.
Pure Mathematics
Y. Puig, Kriz's Theorem via dynamics of linear operators, submitted;
O. Martin, Q. Menet, Y. Puig, Disjoint frequently hypercyclic pseudo-shifts, J. Funct. Anal. 283 (2022), no.1;
Y. Puig, Frequent hypercyclicity and piecewise syndetic recurrence sets, preprint;
A. Aksoy, Y. Puig, Ideal of hypercyclic operators that factor through ell_p, Proc. Amer. Math. Soc. 150 (2022), 691-700;
O. Martin, Y. Puig, Existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing, J. Math Anal. Appl. 500 (1)(2021)125106;
J. Bes, Q. Menet, A. Peris, Y. Puig, Strong transitivity properties for operators, J. Differential Equations, 266 (2019), no. 2-3, 1313-1337;
Y. Puig, Linear dynamics and recurrence properties defined via essential idempotents of the Stone-Cech compactification of N, Ergodic Theory Dynam. Systems, 38 (2018), no.1, 285-300;
Y. Puig, A mixing operator T such that (T, T^2) is not disjoint transitive, Studia Math. 237 (3) (2017), 283-296;
J. Bes, Q. Menet, A. Peris, Y. Puig, Recurrence properties of hypercyclic operators, Math. Ann. 366 (2016), 545-572.
L. Luperi Baglini, Y. Puig, Non-standard methods and finite embeddability in linear dynamics, in preparation.
Latinx Research Project, Caltech, CA
W. Astaiza, A. J. Barrios, H. Chimal-Dzul, S. R. Garcia, J. de la Luz, V. H. Moll, Y. Puig, D. Villamizar, Symmetric tensor powers of graphs (submitted)