
The fourth edition of the Hypatia Graduate Summer School took place from 16 to 19 June 2025 in Barcelona. Addressed to PhD students, the school combined two advanced courses in number theory with a public colloquium, a film screening, and networking activities such as a research speed dating session.
From 16 to 19 June 2025, the CRM and the Institut d’Estudis Catalans hosted the fourth edition of the Hypatia Graduate Summer School, a training programme addressed to PhD students in mathematics. Organised by BGSMath, the graduate training unit of the Centre de Recerca Matemàtica, the school offers an intensive introduction to selected topics, combining formal lectures with opportunities for discussion and exchange.
This year’s edition featured two advanced courses. The first, led by Henri Darmon (McGill University) and Victor Rotger (UPC–CRM), focused on rational points on elliptic curves and deformations of modular forms. The sessions revisited the construction of algebraic points on elliptic curves from the perspective of the Birch and Swinnerton-Dyer conjecture and the Gross–Zagier formula, with particular emphasis on settings beyond complex multiplication. The course introduced participants to recent advances in p-adic methods and modular generating series that offer new strategies for identifying rational points in more general arithmetic contexts.
The second course, taught by Özlem Imamoğlu (ETH Zurich) and Paloma Bengoechea (UB–CRM), explored periods of modular functions over closed geodesics. Starting from the classical theory of complex multiplication and the algebraicity of singular moduli, the lectures extended the discussion to values of modular functions at real quadratic irrationals, defined via integrals over geodesics on the modular surface. The course combined proven results with current conjectures, opening a window onto an emerging area of research at the intersection of number theory and geometry.
One of the highlights of the programme was the Hypatia Colloquium, held at the IEC. In his talk “Modularity and other aspects of the Langlands program: walking in Wiles’ footsteps”, Luis Dieulefait (UB–CRM) presented a panoramic view of the development of modularity results over the past three decades, from Wiles’ proof of Fermat’s Last Theorem to recent generalisations of Serre’s conjecture and base change theorems. The colloquium also introduced the Rayuela conjecture, a proposal aimed at unifying several threads in the Langlands programme.
On its first afternoon, the school offered a screening of Le théorème de Marguerite (dir. Anna Novion, 2023), a French film portraying the personal and academic challenges of a young mathematician. The screening was followed by an informal group discussion.
Beyond its academic programme, the school provides a setting for community building among early-career researchers. On the third day, participants took part in a research speed dating session, in which participants rotated through short conversations in pairs. The goal of the activity was to encourage interaction across institutional and disciplinary boundaries, offering PhD students the chance to expand their professional network in an informal setting.
With more than 40 participants from institutions across Europe and North America, the Hypatia Graduate Summer School continues to serve as a platform for doctoral training, combining specialised content with opportunities for exchange and collaboration.
|
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...
The CRM hosts a new edition of the Barcelona Introduction to Mathematical Research summer school
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...
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...