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. In my thesis I am studying 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
- (with O. García-Prada and M.S. Narasimhan), Higgs bundles twisted by a vector bundle, (arxiv:2105.05543). (See poster).
- Universal spectral covers and the Hitchin map, TEMat monográficos, 2: Proceedings of the 3rd BYMAT Conference (2021) 107-110.
- Higgs bundles twisted by a vector bundle, Máster en Matemáticas Avanzadas, Universidad Complutense de Madrid (2019). (See slides).