
From June 30 to July 25, 2025, the CRM is organising a new edition of the Barcelona Introduction to Mathematical Research (BIMR), a summer school hosted at the Universitat Autònoma de Barcelona. The programme brings together 30 undergraduate mathematics students to explore research through hands-on projects, introductory minicourses, and mentoring activities. With over 20 research topics offered, ranging from analysis and dynamical systems to geometry, cryptography, and mathematical modelling, BIMR provides early exposure to the research environment in an engaging and collaborative setting.
From June 30 to July 25, the Universitat Autònoma de Barcelona is hosting a new edition of the BIMR 2025 – Barcelona Introduction to Mathematical Research summer school. This initiative is promoted by the BGSMath, the CRM’s training unit. The programme offers 30 undergraduate mathematics students the opportunity to engage with mathematical research for the first time, working side by side with active researchers.
At the heart of BIMR are the research projects, assigned according to the preferences of both students and supervisors. This year’s edition features over 20 projects across a wide range of fields, including analysis, PDEs, dynamical systems, algebra, geometry, cryptography and mathematical modelling. Participants will work on topics such as Gamma-convergence, braid theory, Hausdorff measures, optimal control systems, Baker domains, and chaotic dynamical systems applied to cryptography.
Four minicourses to open the doors to research
During the first two weeks, students attend four introductory minicourses, designed to provide an accessible yet rigorous view of cutting-edge topics in mathematics:
Introduction to Stallings automata and the geometry of subgroups of free groups, taught by Enric Ventura and Jordi Delgado (UPC), explores a geometric and algorithmic approach to studying subgroups of free groups. Using intuitive graphical representations and avoiding overly formal language, the course covers key results such as the Nielsen–Schreier theorem, the Schreier index formula, and the Hanna–Neumann inequality.
Markov chains, mixing times and applications, with Guillem Perarnau (UPC – CRM), offers an introduction to discrete Markov chains with a special focus on the concept of mixing time. The course combines spectral theory with classical examples (such as random walks on graphs) and explores applications in statistical physics and theoretical computer science.
Singular integrals, Hausdorff measures and capacities, taught by Laura Prat (UAB), introduces fundamental tools in harmonic analysis and geometric measure theory. The course covers Calderón-Zygmund integrals, Hausdorff measures applied to fractal sets, and various notions of capacity with applications in the study of removable sets and partial differential equations.
Mathematical modelling of cancer as an ecological and population dynamics system, with Tomás Alarcón (CRM), presents an innovative perspective on cancer biology through the lens of mathematics. The course shows how ecological tools and dynamical systems theory can help understand tumour behaviour as evolving ecosystems.
Beyond mathematics
In addition to the academic programme, BIMR 2025 includes social and mentoring activities, such as a round table on academic careers, a public outreach talk, and weekly informal gatherings. For students living outside the metropolitan area of Barcelona, the CRM offers accommodation fellowships throughout July.
With this programme, BIMR aims to bring the research experience closer to a new generation of mathematicians and help spark scientific vocations early in their careers.
The programme is organised by Natàlia Castellana (Universitat Autònoma de Barcelona, CRM), Marc Masdéu (Universitat Autònoma de Barcelona, CRM), Xavier Ros-Oton (Universitat de Barcelona, ICREA, CRM) and Olli Saari (Universitat Politècnica de Catalunya, CRM), with the support of the BGSMath network.
Subscribe for more CRM News
|
CRM CommPau Varela
|
Mathematics Beneath the Tarmac: CRM’s Role in Enhance Europe
The Centre de Recerca Matemàtica (CRM) participates in Enhance Europe. This European research project explores how solar heat from asphalt can be harvested and reused as thermal energy in cities. Through its Knowledge Transfer Unit, CRM leads the...
Talent jove al CRM: tres estudiants del programa Joves i Ciència fan estada a la Unitat de Transferència
D'esquerra a dreta: Lucía Escudero, Clara Castelló, Marc Homs-Dones, Roger Carrillo, Manel Mas, Maria Borrell i David Romero. Per segon any, la Unitat de Transferència del CRM ha acollit tres estudiants del programa Joves i Ciència de la Fundació...
BAMB! 2025: A School for Models, Minds, and the Messy Art of Behavior
BAMB! 2025 brought together thirty early-career researchers in Barcelona for an intense nine-day training on model-based analysis of behaviour. Organised by the Centre de Recerca Matemàtica with top international researchers, the school combined...
Barcelona, Stochastic Analysis and Quantitative Finance: Highlights of the 2025 Summer School
The 5th edition of the Barcelona Summer School on Stochastic Analysis and Quantitative Finance took place from July 21 to 25, 2025, at the Centre de Recerca Matemàtica (CRM), marking the revival of an academic tradition interrupted by the pandemic. The program offered...
Scientific vision and dialogue: the SAB meets at CRM to advise on future directions
The Scientific Advisory Board of the CRM met in July 2025 to advise on the centre’s scientific direction and review key aspects of its activity. In addition to looking at strategic plans and recruitment priorities, Board members took part in a...
Mathematics Illuminates Metabolic Mysteries: Understanding SDH-b Dysfunction in Pheochromocytoma
A mathematical model developed by researchers from the University of Birmingham, Queen Mary University of London, and the Centre de Recerca Matemàtica reveals how chromaffin cells adapt to the loss of SDH-b—a key metabolic enzyme subunit whose dysfunction is linked to...
ESGI 2025: Mathematics Meets Industry at the CRM
Over the course of five days, ESGI 2025 turned the CRM into a collaborative lab where mathematics tackled questions raised by industry. From safer autonomous driving systems to smart water resource allocation and the financial uncertainties of wind...
Quatre noves figures s’incorporen a l’exposició del CRM sobre dones matemàtiques
Aquest estiu, el CRM ha ampliat fins a tretze els roll ups de la seva exposició sobre dones matemàtiques, incorporant quatre noves figures del context espanyol i català. La mostra aprofita l’afluència de visitants al centre per visibilitzar...
From Real Problems to Mathematical Applications: A Chronicle of the XI Iberian Modeling Week
From July 7 to 11, the CRM became a hub for collaborative problem-solving during the XI Iberian Modeling Week, an international training initiative that brought together nearly 30 students from diverse academic backgrounds to tackle real-world...
The Way DNA Folds Might Help Explain How Cells Decide What to Become
A new study by researchers from the University of Edinburgh, Oxford, and CRM reveals how the 3D structure of DNA and a microscopic molecular tug-of-war shape the identity of every cell in our...
Niclas Rieger defends his PhD thesis on data-driven climate analysis and marine pollution
Niclas Rieger defended his PhD thesis at the Institut de Ciències del Mar, culminating a research journey focused on extracting insights from both massive climate datasets and scarce environmental observations. Developed within the European CAFE...
A Day of Higher Structures in Symplectic and Poisson Geometry, with Summer Tapas at UPC Barcelona
The event "A Summer Tapas Invitation to Higher Structures in Symplectic and Poisson Geometry I", held on July 7, 2025, at EPSEB–UPC, featured talks by Alejandro Cabrera, Chenchang Zhu, Miquel Cueca, and Mario Garcia-Fernandez, offering a rich and informal exploration...