About me

I  hold a degree in Mathematics and a degree in Physics from the Complutense University of Madrid. I have been always very interested in topology and geometry: my final dissertation for the degree in Mathematics (supervised by María Pe Pereira) was about singularities in complex hypersurfaces. In particular, I studied a construction due to Milnor that describes a locally trivial fibration surrounding such singularities. The full text in Spanish can be found here.

I continued working on that project the following year during my MSc in Advanced Mathematics at the Complutense University. I was awarded a research Collaboration Grant from the University to carry out such research. My final thesis for these graduate studies, again supervised by María Pe Pereira, concerns the monodromy of isolated singularities in complex hypersurfaces. 

From 2021 to 2025 I completed a PhD programme at the London School of Geometry and Number Theory, a Centre for Doctoral Training joinning University College Londong, King's College London and Imperial College London. At the LSGNT we have a largely taught first year, during which we have to fulfil two mini-projects of research. 

• My first mini-project was a joint work with Nick Manrique in Understanding the proof of Lawson's Conjecture, under the supervision of Marco Guaraco and Costante Bellettini. Lawson's Conjecture was a very renowned conjecture in the field of minimal surfaces, due to H. Blaine Lawson. It states that the only surface with genus 1 minimally embedded in the three-dimensional sphere is the so-called Clifford torus. This fact was conjectured by Lawson in 1970, but it was not until 2012 that it was proved by Simon Brendle. In this work, we reviewed this proof and the theory of minimum principles of two-point functions, which plays a crucial role in it. 

• My second mini-project was under the supervision of Anthea Monod and consisted on harnessing the state-of-the-art for persistent homology computation by studying the problem of determining topological prevalence and cycle matching using a cohomological approach, which increases their feasibility and applicability to a wider variety of applications and contexts. This paper is the final result of such project.

From the second year of my PhD I was based at Imperial College working under the supervision of Anthea Monod in Topological Data Analysis. In my thesis, I have focused in different facets of persistent homology, a mathematical tool that helps uncover the hidden shape and structure of data. It turns complex datasets into visual summaries called persistence barcodes, which track how features like clusters, loops, and voids appear and disappear at different scales in the data. My work explores how duality principles shape this theory, how functional invariants can connect it with modern statistics, and how these ideas can power new approaches in deep learning. The full text can be found here. 

Outside of maths I love cooking (and impulse buying cookbooks), practising yoga and running, and going to musicals, theatre and the opera. I also love signing: I joined the Imperial College Choir on 2022, and have been part of its committee from 2023 to 2025.