My line of research lies at the interface of mathematics and theoretical quantum physics, and primarily concerns proving analytical results for strongly correlated quantum many-body systems from a quantum information perspective. I am particularly interested in the structure of tensor network states and their symmetries, the different classification programmes of quantum phases of matter, the description of the topological order phenomena, the properties of quantum thermal states and dissipative quantum evolutions, and the abstract theory of quantum groupoids, fusion categories, and operator algebras.

 

Since February 2024, I am a postdoctoral researcher at Complutense University of Madrid and the mathQI group, supported by a contract within the Quantum Spain project and under the supervision of Prof. David Pérez García, with the objective of investigating the internal symmetries and convergence of dissipative process in quantum many-body and quantum-inspired systems related to tensor networks.

 

Previously, I held a postdoctoral fellow position at University of Tübingen, under the guidance of Prof. Ángela Capel and Prof. Dr. Stefan Teufel, as part of the CRC TRR 352 project, where we focused on analyzing the decay of correlations and the response to local perturbations exhibited by quantum thermal states.

 

I started my academic education with a Bachelor's degree in Mathematics from Complutense University of Madrid, followed by a Master's degree in Advanced Mathematics at the same university, with undergraduate and master thesis on measure and metric space theory. Afterwards, I began my doctoral studies at Complutense University of Madrid under the supervision of Prof. David Pérez García and Dr. András Molnár, supported by a Severo Ochoa Research Personnel Training (FPI-SO) contract at the Institute of Mathematical Sciences (ICMAT), Spanish National Research Council (CSIC). During my studies I carried out a four-month stay in the group of Univ.-Prof. Dr. Norbert Schuch at the University of Vienna. I defended my thesis in January 2023, titled «Weak Hopf algebras, matrix product operators and the classification of quantum phases of matter», devoted to establishing connections with algebraic structures in quantum many-body systems in order to better understand their symmetries, topologically ordered phases and the classification of quantum phases of matter in open systems.

 

You can also find me on Google Scholar, ORCiD, and arXiv.