Profesora Contratada Doctora (Associate Professor)
Department of Algebra, Geometry and Topology
School of Mathematical Sciences
Complutense University of Madrid
Algebraic Geometry and Applications to Mathematical Physics

 

 

 

Bio

2022 Research Professor, Mathematical Sciences Research Institute, Berkeley, USA (August to December).
2021– Associate Professor (Profesora Contratada Doctora), Universidad Complutense de Madrid, Spain.
2020— Fellow of the Institute of Mathematics and Applications, UK.
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), Consejo Superior de Investiga- ciones Cient ́ıficas, Instituto de Ciencias Matema ́ticas, Madrid, Spain.
2010–14 Honorary Professor, Universidad Auto ́noma de Madrid, Madrid, Spain.
2007–09 FTC Postdoctoral Researcher, Centro de Matema ́tica da Universidade do Porto, Porto, Portugal.
2006–07 Postdoctoral Researcher, Max Planck Institut fu ̈r Mathematik, Bonn, Germany.2006 PhD. in Mathematics, Universidad Autónoma de Madrid.

 

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 and singular curves.

 

Grants (past 5 years)

 

Latest Publications

• Stratification of SU(r)-character varieties of twisted Hopf Links, (with A. González-Prieto, J. Martínez, V. Muñoz), Moduli Spaces and Vector Bundles—New Trends, Contemporary Mathematics volume 803, (2024), 257–278.
• On character varieties of singular manifolds, (with A. González-Prieto), accepted in Research in the Mathematical Sciences (2023)
• Symplectic geometry of a moduli space of framed Higgs bundles, (with I. Biswas and A. Peón-Nieto), IMRN Volume 2021, Issue 8, (2021), 5623–5650.
• A lax monoidal Topological Quantum Field Theory for representation varieties, (with A. González- Prieto and V. Muñoz), Bull. Sci. math. 161 (2020) 102871.
• Moduli spaces of framed G–Higgs bundles and symplectic geometry, (with I. Biswas and A. Peón- Nieto),  Comm. Math. Phys. 376 (2020), no. 3, 1875–1908.
• On Higgs bundles on nodal curves, SIGMA Symmetry Integrability Geom. Methods Appl. 15 (2019), 024, 16 pages.

 

Grants and project evaluator for:

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