## 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).