"When he [Oscar Zariski] spoke the words 'algebraic variety', there was a certain resonance in his voice that said distinctly that he was looking into a secret garden. I immediately wanted to be able to do this too. It led me 25 years of struggling to make this world tangible and visible."
David B. Mumford
My research lies within the fields of algebraic geometry and low-dimensional topology. More precisely, I study the geometry of algebraic varieties parametrizing group representations and their associated moduli spaces, known as representation and character varieties, with particular emphasis on their interplay with knot theory.
I focus on computing motivic invariants of these spaces, such as mixed Hodge polynomials and virtual classes, as well as exploring the connection between these algebraic varieties and knot invariants, especially Alexander type invariants.
Keywords: representation varieties, character varieties, twisted Hopf links, Alexander invariants, Grothendieck ring.
Preprints
Á. Molina-Navarro, Stratification of AGLr(C)-representation varieties of twisted Hopf links. arXiv:2605.13585, 2026.
Here you will find notes on various topics related, in some way, to my research. I hope they will help anyone trying to better understand these subjects.
A detailed, self-contained proof of the Riemann-Hilbert correspondence in its classical setting.
Master's thesis: Moduli and varieties of group representations, supervised by Dr. Vicente Muñoz (MSc Thesis, Slides)
[Awarded the maximum possible grade]
Bachelor's thesis: Extensions of modules (in Spanish), supervised by Dr. Manuel Saorín and Álvaro Campillo (BSc Thesis, Slides)