Research interests
My research lies within the field of algebraic and differential geometry. More precisely, I am interested in moduli spaces of principal bundles with additional structure. During my PhD I studied several generalizations of the Hitchin system, which is an algebraic completely integrable system on the cotangent space of the moduli space of vector bundles over a compact Riemann surface. This was introduced by Nigel Hitchin in his 1987 seminal paper.
Related topics include:
- Gauge theory
- Higgs bundles
- Spectral and cameral covers
- Representations of surface groups
- Higher Teichmüller theory
- Langlands duality
- Moment maps and infinite-dimensional manifolds
- Geometric invariant theory
- Moduli stacks
Here you can find a more detailed Research Statement.
PhD thesis
- Multiplicative Higgs bundles, monopoles and involutions, Doctorado en Investigación Matemática, Universidad Complutense de Madrid. 2023. (See slides).
Publications
- (with O. García-Prada), Multiplicative Higgs bundles and involutions, (arxiv:2304.02553). Advances in Mathematics, Volume 451, 109789, ISSN 0001-8708. 2023. (See slides, video).
- (with O. García-Prada and M.S. Narasimhan), Higgs bundles twisted by a vector bundle, (arxiv:2105.05543). International Journal of Mathematics. 2021. (See poster).
Proceedings
- Universal spectral covers and the Hitchin map, TEMat monográficos, 2: Proceedings of the 3rd BYMAT Conference 107-110. 2021.
Master's thesis
- Higgs bundles twisted by a vector bundle, Máster en Matemáticas Avanzadas, Universidad Complutense de Madrid. 2019. (See slides).