Research Area and Research Interests

Algebraic and complex geometry, algebraic topology and mathematical physics. In particular I study the geometry and topology of moduli spaces arising in geometry and physics. Keywords: Higgs bundles, integrable systems, mirror symmetry, TQFTs, geometric quantisation, shifted Poisson structures, algebraic stacks, coherent systems, Brill-Noether theory and singular curves.

Ongoing Research Projects

Principal Investigator for the project: Geometría algebraica y aplicaciones a la física matemática. Santander-UCM 2021 (2022-2023) PR44/21-29924 10.367,85 €

Co-Principal Investigator for the project: Algebraic Geometry and applications to Mathematical Physics. PID2021-124440NB-I00 (2022-2025) 72.600€

Qualifications

2018 Fellow of the Higher Education Academy.

2014 Habilitation: Profesor Contratado Doctor by ANECA. Recognised by the European Quality Assurance Register for Higher Education.

2006 PhD in Mathematics, Universidad Autónoma de Madrid. Awarded "European PhD" as quality recognition.

Positions

2022 (August - December) Research Professor, Mathematical Sciences Research Institute, Berkeley, USA.

2021-present Associate Professor (Profesora Contratada Doctora), Universidad Complutense de Madrid, Spain.

2019–21 Visiting Professor, Universidad Complutense de Madrid, Spain.

2017–19 Lecturer in Pure Mathematics, University of Plymouth, UK.

2016–17 Marie Curie Individual Fellowship, Mathematical Institute, Oxford, UK.

2010–15 Postdoctoral Research Fellow, (i-Math, JAE-Doc and Severo Ochoa), CSIC, ICMAT, Madrid, Spain.

2010–14 Honorary Professor, Universidad Autónoma de Madrid, Madrid, Spain.

2007–09 FTC Postdoctoral Researcher, Centro de Matemática da Universidade do Porto, Porto, Portugal.

2006–07 Postdoctoral Researcher, Max Planck Institut für Mathematik, Bonn, Germany.