spectral curve

Research

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:

Here you can find a more detailed Research Statement.

PhD thesis

  1. Multiplicative Higgs bundles, monopoles and involutions, Doctorado en Investigación Matemática, Universidad Complutense de Madrid (2023). (See slides).

Publications

  1. (with O. García-Prada and M.S. Narasimhan), Higgs bundles twisted by a vector bundle, (arxiv:2105.05543). (See poster). To appear in the International Journal of Mathematics.

Preprints

  1. (with O. García-Prada), Multiplicative Higgs bundles and involutions, (arxiv:2304.02553). (See slides).

Proceedings

  1. Universal spectral covers and the Hitchin map, TEMat monográficos, 2: Proceedings of the 3rd BYMAT Conference (2021) 107-110.

Master's thesis

  1. Higgs bundles twisted by a vector bundle, Máster en Matemáticas Avanzadas, Universidad Complutense de Madrid (2019). (See slides).