Research

My interests

My research is originally in the field of operator algebras. More precisely, my work concerns the interaction between (quantum) groups and K-theory in the context of the Baum-Connes conjecture. Nevertheless, my research activities have spread to different branches of mathematics thanks to the richness and interdisciplinarity of the subject. This allows me to work on a wide range of problems throughout algebraic topology, C*-algebras, C*-dynamics, homological algebra, module C*-categories, K-theory, (higher) representation theory, tensor triangular geometry and triangulated categories.

In addition, I am developing a great interest for two specific topics:

Quantum Information Theory, Non-local Games and their relation with quantum groups and operator algebras.
Topological Data Analysis and Topological Deep Learning in the context of graphical models.

Doctoral project

"The Baum-Connes conjecture for Quantum Groups. Stability properties and K-theory computations"

The main goal of my thesis (under the direction of P. Fima) has been to compute the K-theory of the C*-algebras associated to compact quantum groups in some (interesting and) concrete examples. The strategy to reach such computations involves the study of the quantum counterpart of the Baum-Connes conjecture.

I achieved my doctoral project in September 2018. Here you can find the manuscript.

Master thesis

My bachelor's dissertation ("Existencia de funciones meromorfas en superficies de Riemann abiertas") is about Behnke-Stein's theorem in dimension 1, that is, the generalization of Runge's theorem about the approximation of holomorphic functions in open Riemann surfaces.

During my master's degree M1 I continued to study in depth complex analysis/geometry and my M1 dissertation ("Analyse Complexe à plusieurs variables. Le théorème de Hartogs") is about Hartogs' theorem of holomorphic extension in complex dimension n>1.

In my M2 master's dissertation ("Groupes agissant sur un arbre et K-moyennabilité. Une introduction à la K-théorie") I studied Kasparov's KK-theory in order to prove the K-amenability of a discrete group acting on a tree with amenable stabilizers (after P. Julg and A. Valette).

Google Sites

Report abuse