Publications

Preprints

Papers

The preprint versions are available in arXiv.

Talks

Invited talks

Contributed talks

Seminars

  • Descomposiciones de politopos y teoremas tipo Banach-Stone para espacios metricos. Seminario de Geometría Diferencial y Convexa. Murcia, February 2022
  • The weak maximizing property and asymptotic geometry of Banach spaces. Functional Analisis Seminar. University of Tartu, April 2021 Video
  • La propiedad maximizante débil y geometría asintótica de espacios de Banach. Seminario Rubio de Francia, Universidad de Zaragoza, Oct 2020
  • The weak maximizing property and asymptotic geometry of Banach spaces. Measure Theory Seminar. Kent State University, September 2020
  • Volume product and metric spaces. Seminar der Arbeitsgruppen Diskrete Mathematik/Geometrie & Diskrete Geometrie. Technische Universität Berlin, May 2020
  • Volume product and metric spaces. Analysis Seminar. University of Rochester, April 2020
  • Stability of Lipschitz-type functions under pointwise product and reciprocation. Karcher Colloquium. University of Oklahoma, March 2020
  • Volume product and metric spaces. Analysis Seminar. University of Oklahoma, March 2020
  • Volume product and metric spaces. Analysis and Applied Math Seminar. University of Toronto, February 2020
  • On strongly norm attaining Lipschitz maps. Analysis seminar. University of Illinois at Urbana-Champaign, December 2019
  • On strongly norm attaining Lipschitz maps. Geometry Luncheon Seminar. Penn State University, State College, November 2019
  • Volume product and metric spaces. Analysis and Probability Seminar. Case Western Reserve University, Cleveland, Oct 2019
  • Geometry and topology around extreme points. Graduate Student Seminar. Kent, Oct 2019
  • On strongly norm attaining Lipschitz maps. Workshop in Analysis and Probability Seminar. Texas A&M, July 2019
  • Producto de volúmenes para bolas de espacios de funciones Lipschitzianas. Seminario Rey Pastor. Murcia, December 2018
  • Extreme points in Lipschitz-free spaces. Colloquium. Kent, December 2018.
  • Lyapunov's theorem and application to fair cake-cutting. Non-Linear Analysis Seminar. Kent, November 2018.
  • Strongly norm-attaining Lipschitz maps. Measure Theory Seminar. Kent, Nov 2018.
  • Estructura extremal de espacios Lipschitz libres. Seminario de jóvenes investigadores en Matemáticas. Granada, February 2018.
  • Compact convex sets that admit a strictly convex function. I Jornadas de Doctorandos en Matemáticas. Murcia, September 2016.
  • Aplicaciones con la propiedad de Radon-Nikodym. Seminario del Departamento de Análisis Matemático. Granada, December 2016.
  • Puntos expuestos de continuidad para una función estrictamente convexa. Seminario de jóvenes investigadores en Matemáticas. Granada, November 2016.
  • Asymptotic uniform smoothness in spaces of compact operators. Séminaire d’Analyse fonctionnelle. Besançon, March 2016.

Posters

Thesis

Convexity, Optimization and Geometry of the Ball in Banach Spaces

The research done during my PhD involves several topics in the framework of the geometry of Banach spaces. The guiding theme is the structure of convex sets. Several properties based on the notions of extreme and exposed points are analyzed. This includes classical properties as the Radon-Nikodym property, which is studied from a non-linear point of view, as well as the study of the geometry of the norm in tensor products. Moreover, some isometric properties (in particular, the Daugavet property and the extremal structure) are studied in spaces of Lipschitz functions and their preduals. These last spaces, known as Lipschitz-free spaces, are a very active research topic by their applications in non-linear analysis. The research has been done in collaboration with the reasearch groups of Murcia and Granada (Spain) and Besançon (France). To this end, a three months research stay was done in Besançon, and a two-weeks research stay was done in Granada.

My thesis was supervised by Bernardo Cascales and Matías Raja.

(comics from xkcd and Spiked Math)