Director, CRM
“2025 was a productive year for our research — and a year in which we set out where the institution is heading through our new 2026–2030 Strategic Plan.”
Our scientific programme is now organised around four core areas — algebra & geometry, analysis, PDEs & dynamical systems, mathematical modelling and combinatorics — with flagship work at the intersection of AI and mathematics.
In December the centre successfully completed its four-year CERCA evaluation. We launched the CRM–MdM Chair of Excellence to host senior women researchers, and continued our public engagement through the podcast Ments Meravelloses and the blog El Gegant del π.
From 66 countries, across six continents.
In 2025 the CRM welcomed researchers and students from around the world for programmes, schools and extended research stays — over 1,400 participants in all.
Ten groups, one mathematical hub.
CRM researchers are based at the centre and across Barcelona’s universities — the UAB, UPC and UB — with several holding ICREA affiliations, and they converge on the CRM through shared programmes, seminars, visiting scientists and its graduate school. Select a group to see its members, projects and publications.
Algebra and Algebraic Geometry
Non-commutative and commutative algebra, moduli spaces, Arakelov geometry and abelian varieties.
Geometry and Topology
Differential and symplectic geometry, algebraic topology — including an abstract “fluid computer.”
Number Theory
Deep arithmetic phenomena through the lens of the Langlands Program — Galois representations, automorphic forms and abelian varieties.
Mathematical and Computational Biology
New theory, models and tools for biologists and clinicians — multiscale models, dynamical systems and machine learning.
Computational and Mathematical Neuroscience
Systems-level neuroscience: how large assemblies of interacting neurons give rise to animal and human behaviour.
Mathematics for the Environment and Society
Mathematical and statistical techniques for natural hazards, climate and the capture of environmental contaminants.
Analysis
Classical analysis at the interaction of complex and harmonic analysis with geometric measure theory, PDEs and probability.
Partial Differential Equations
Regularity of nonlinear PDE, free boundary problems, minimal surfaces and nonlocal equations from probability and physics.
Dynamical Systems
Invariant objects and their connections, with applications in celestial mechanics, astrodynamics, neuroscience and chemistry.
Combinatorics and Mathematics of Computer Science
Discrete mathematics, theoretical computer science and mathematical logic — from graph theory to computational complexity.
Thirteen from 140 papers.
The results the centre highlighted from its 2025 output, spanning the research groups. Each links to the paper.
On Darmon’s program for the generalized Fermat equation, I
Carleson’s ε²-conjecture in higher dimensions
Representational drift as the consequence of ongoing memory storage
Asymmetry of MHD equilibria for generic adapted metrics
Stable solutions to the fractional Allen–Cahn equation
Generating heterogeneous data on gene trees
Ergodic properties of infinite extensions of interval exchange maps
Improvement of flatness for nonlocal free boundary problems
Solvability of the Poisson–Dirichlet problem in Carleson spaces
Multiscale modelling of cell–ECM interactions
Hochschild polytopes
Consistency of Relations over Monoids
A homogenized model for dispersive transport and sorption
Turning theorems into tools.
The Knowledge Transfer Unit connects CRM research with companies, institutions and the public sector — building tailored solutions in modelling, simulation, optimisation and data science, and running two industrial study weeks each year.
BISTECH
A mathematical model — and a friendly interface — for cooking a wide range of foods with a new device.
DYSEDAS
A lossless data-compression method powered by dynamical systems, with the ALBA Synchrotron as end user.
LICSAI
Quantifying the uncertainty of an AI algorithm that estimates the risk of a phishing attack.
TIPSAVIR
Simulating viral infection at the RNA level to search for therapeutic interfering genomes as antivirals.
eBRT2030
A Horizon Europe project with 49 partners developing a new generation of electric Bus Rapid Transit systems.
David Romero (Head) · Lucía Escudero · Marc Homs-Dones · Manel Mas · Daniel Cuadrillero
ICFO · ICM · ALBA Synchrotron
A timeline of 2025.
4th Nonlinear Processes in Oceanic & Atmospheric Flows
An international forum bringing together mathematicians, physicists and oceanographers on the nonlinear dynamics of atmospheric and oceanic phenomena (22–25 January).
BCN Face(t)s in Symplectic Geometry
The year opens with a symplectic-geometry meeting in Barcelona (28–31 January), organised by Eva Miranda.
Barcelona Discrete Mathematics Meeting
Seven Barcelona discrete-maths groups meet for a day of talks (30 January) to spark new collaborations — the first BDMM.
Workshop on Discrete Dynamical Systems
A workshop revisiting difference equations, topological and combinatorial dynamics (3–6 February).
New Frontiers in Homogenization & Fractional Calculus
A meeting on homogenization and fractional calculus (24–25 March), with Xavier Cabré on the programme committee.
Chair of Excellence launches
The CRM–María de Maeztu Chair of Excellence opens with an inaugural colloquium by Chenchang Zhu (Göttingen) on higher structures in symplectic geometry (9 April).
BARCCSYN 2025
The 13th Barcelona Computational, Cognitive & Systems Neuroscience meeting (22–23 May).
PDE in Barcelona
The analysis and PDE community gathers at the Universitat de Barcelona, organised by Xavier Ros-Oton and Tomás Sanz-Perela.
Topics in Complex Dynamics 2025
A week connecting complex dynamics to geometry and analysis at the Universitat de Barcelona (2–6 June).
Jornada de Ciència Oberta
An open-science day on transparency and accessibility across the whole research process (11 June).
Hypatia 2025 Summer School
A graduate summer school in number theory with a gender perspective highlighting women in mathematics (16–19 June).
Harmonic Analysis & PDEs Summer School
A summer school on singular integrals, fluid mechanics and interaction-energy minimisers (25–27 June).
BIMR 2025
The Barcelona Introduction to Mathematical Research summer school gives undergraduates a first taste of research (30 June–25 July).
European Study Group with Industry
ESGI 2025 (14–18 July) pairs mathematicians with companies to solve real industrial problems, back-to-back with the Modeling Week.
5th BCN Summer School of Stochastic Analysis & Mathematical Finance
Advanced courses reviving the CRM’s stochastic-analysis summer-school series (21–25 July).
Strategic Plan 2026–2030
The Scientific Advisory Board approves the new strategic plan, setting the centre’s direction across research, training and community.
Bilbao–Barcelona Analysis & PDEs
A joint analysis and PDEs meeting co-organised with BCAM in Bilbao (3–5 September).
New ATRAE researcher
A new ATRAE researcher joins the centre in September as part of ongoing talent attraction and diversity efforts.
Complex Systems Society School
The first school of the Complex Systems Society Spain (CS3), on the science of complex systems (29 September–3 October).
XIII GEFENOL–DIFENSC Summer School
A summer school on the statistical physics of complex systems (6–10 October).
Advanced graduate courses
BGSMath graduate courses run on Concentration Inequalities for Holomorphic Functions (27 Oct–5 Nov) and on the P vs NP problem (3–14 Nov).
100xCiencia · Knowledge transfer
CRM Director Carme Cascante and KTU head David Romero join the SOMMa 100xCiencia meeting in Valencia (13–14 November), on science communication and knowledge transfer.
CERCA evaluation passed
The centre successfully completes its four-year CERCA evaluation, conducted by an international committee.
Recognition on the world stage
Jezabel Curbelo receives the National Research Award for Young Researchers; Xavier Tolsa, Joaquim Ortega-Cerdà and Xavier Cabré are invited to ICM 2026 — Tolsa as a plenary speaker.