I am a Professor of Mathematical Analysis at the University of Barcelona since 2011. My research focuses on complex and harmonic analysis in one and several variables, particularly on the study of the inhomogeneous Cauchy-Riemann equation to address problems such as the size of the Bergman kernel. It also addresses the description of zero sets, interpolation sequences, and sampling sequences. Other lines of research I am interested in include Dirichlet series, viewed from the perspective of function theory in the infinite-dimensional polydisk, and more recently, random point processes and optimal point configurations, as well as extremal problems in Fourier analysis.
I was an invited speaker at the 7th European Congress of Mathematics in Berlin and received the Journal of Complexity Best Paper Award in 2016. Since January 2025, I have been a fellow of the Royal Norwegian Society of Sciences and Letters (DKNVS). I have also been awarded the ICREA Academia distinction for the period 2025–2030. Recently, I was invited to give a lecture in the Mathematical Analysis section of the International Congress of Mathematicians (ICM), to be held in Philadelphia in July 2026.
My main contributions can be summarized as follows:
A metric/geometric description of sampling and interpolation sequences in various spaces of holomorphic functions. This problem lies at the mathematical foundation of signal analysis, and my contributions have been developed in a long series of papers (among them in J. Reine and GAFA) with several co-authors, culminating in the solution of a problem posed in 1952 by Duffin and Schaeffer, which characterizes the exponential functions that form a basis in L2L^2 of an interval. This work was published in Annals of Mathematics in 2002.
Optimal inequalities in function spaces. The study of optimal inequalities for functions defined on the polydisk with constants that are controlled and independent of the dimension is very useful for transferring inequalities to the infinite-dimensional polydisk. Once this is achieved, Bohr's lifting scheme can be used to obtain inequalities for Dirichlet series that are of interest in analytic number theory. Two representative papers in this line of research are "The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive", published in Annals of Mathematics in 2011, where an inequality for homogeneous polynomials on the polydisk, originally proven by Littlewood in 1929 for bilinear forms, is extended with the correct constant to multilinear forms; and a more recent work, published in GAFA in 2021, titled "Idempotent Fourier multipliers acting contractively on HpH^p spaces."
A systematic study of point equidistribution on varieties, via deterministic and random point processes. The most notable results in this area are "Equidistribution estimates for Fekete points on complex manifolds" (JEMS, 2016) and "A sequence of polynomials with optimal condition number" (J. Amer. Math. Soc., 2021). In the latter, a problem posed by Shub and Smale in 1993 was solved, concerning the search for polynomial roots well distributed on the sphere. The associated polynomial is well-conditioned as a starting point for a Newton method to find polynomial roots.
Throughout my career, I have served on various editorial boards, including Collectanea Mathematica, Revista Matemática Iberoamericana, Journal of Fourier Analysis and Applications, Constructive Approximation, and Analysis and Mathematical Physics.
I have contributed to research management as Director of the Institute of Mathematics at the University of Barcelona (IMUB), coordinator of scientific activities at the Centre de Recerca Matemàtica (CRM), and Vice President of the Catalan Mathematical Society (SCM). I have organized numerous conferences and workshops, notably two thematic semesters on Analysis at the CRM, which included conferences, workshops, and advanced courses.
I have published around 75 research papers, some in top mathematical journals such as J. Amer. Math. Soc., Annals of Mathematics (2), J. Eur. Math. Soc., Amer. J. Math., GAFA (2), Crelle's Journal, and Journal de Mathématiques Pures et Appliquées. I have also presented my results in over 100 invited talks at various conferences.
