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JUAN

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Grupo de investigacion
Geometría y sus aplicaciones
Member
2021-10-05
University Department
MATEMÁT. E INFORMÁT. APLICADAS
Profesor Permanente Laboral
2024-02-08

Brief description ot the activity

I am currently an Associate Professor (Prof. Permanente Laboral) at the Universidad Politécnica de Madrid, previously serving as Assistant Professor (Prof. Ayudante Doctor) since 2020. My research interests include singularity theory, low-dimensional topology, motivic integration, zeta functions, and topology of complements.

I earned my PhD in Mathematics in 2015 at the University of Pau (France) through a joint program with the University of Zaragoza (Spain) under the supervision of Jacky Cresson and Enrique Artal. My academic background includes two Master’s theses: one on knot theory and algebraic topology (University of Pau) and another on computational aspects of zeta functions of non-degenerated polynomials (University of Zaragoza). My PhD research focused on singularities in real and complex algebraic geometry, their links to number theory and dynamical systems, and algorithmic approaches implementable in SageMath. This work was supported by French and Spanish public funding and fostered collaborations with researchers in France, Spain, and Japan.

After my PhD, I obtained several international postdoctoral grants to study singularity theory, including the topology of line arrangements and invariants from motivic integration and zeta functions. I also developed an external SageMath library based on my master’s thesis.

My research production includes 8 publications and 2 preprints, with two major papers in Q1 JCR journals:
 - Mathematische Annalen: “Configurations of points and topology of real line arrangements” (with Benoît Guerville-Ballé), introducing a large family of Zariski pairs and showing unexpected flexibility in real complexified line arrangements.
 - Advances in Mathematics: “Motivic zeta functions on Q-Gorenstein varieties” (with Edwin León Cardenal, Jorge Martín Morales & Wim Veys), providing formulas for motivic and topological zeta functions via partial toric resolutions, reducing combinatorial complexity and enabling progress on the Monodromy Conjecture.

I presented these results at major events, including the Congreso bienal de la Real Sociedad Matemática Española (2017) and the International Congress of Mathematicians (ICM 2018) in Rio de Janeiro. I have also given invited talks and mini-courses at leading institutions such as IMPA (Brazil) and participated in conferences and seminars across Spain, France, Mexico, Brazil, and Japan.
Currently, I lead academic planning for UPM’s Mathematics Degree (EPES), manage communication and the program website, and co-supervise Bachelor’s theses at UPM and Universidad Complutense de Madrid. I am also involved in innovative teaching projects, including randomized exercises and exams.

I actively organize international events for young researchers, specially the IberoSing Workshops (2022–2024) on topics such as Low-dimensional Topology, Mirror Symmetry, and Singularity Theory at UPM, Universidad de Granada, and Universidad Complutense de Madrid.

Frequent topics

Timeline

Research sections
1
Last granted: 2025

Publications

Agencies
Number of Documents
N Citations
h-index
Q1
D1
IFNA
IFNB
IFNESI
WoS
December 2025
5
9
2
1
-
0.25
0.26
0.19
Scopus
December 2025
6
12
3
2
2
0.17
0.14
-
Porcentaje en Q1 1/5
Porcentaje en D1 2/10

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Almetrics publications

Publications in social networks: 0 / 6
Percentage: 0.00%
Score: 0
Average score:
0 / 6 = 0.000

I+D+I Projects

Miembro
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Final project (Bachelor)
4

Subject / Course

Institutional collaboration last 5 years

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