From 23 June to 4 July 2025, the Institute of Mathematical Sciences (ICMAT) hosted a new edition of the JAE School of Mathematics, attended by 86 undergraduate and Master’s students from national and international universities. Over the course of two weeks, participants had the opportunity to explore current topics in mathematical research through mini-courses and talks delivered by renowned experts. This initiative is part of ICMAT’s commitment to the training of young researchers and was held alongside the 2025 Severo Ochoa Introductory Research Fellowships programme.
A total of 86 undergraduate and Master’s students took part in the 2025 JAE School of Mathematics. Images: Laura M. Iraola/ICMAT
From 23 June to 4 July 2025, 86 final-year undergraduate and Master’s students (30.4% of them women) had the chance to engage directly with cutting-edge research topics and professionals at the JAE School of Mathematics at ICMAT. “Over the course of these weeks, a fruitful interaction was established between top-level researchers and students who enjoy mathematics, in an exceptional environment,” said the organisers.
“What matters most at these events is not just the exchange between students and lecturers, but also among the students themselves,” said Ana Rechtman (University of Grenoble, France), one of the lecturers at the 2025 JAE School. “For the training of future researchers, human, face-to-face exchanges such as this school are essential,” she added. Although the majority of the 2025 JAE School students came from Spanish universities (65% from Madrid, but also from Barcelona, Zaragoza, Granada, Santiago de Compostela, Alicante, Valladolid, Oviedo and Bilbao), this year’s cohort also included students from Sorbonne University (France), Brown University (USA), Federal University of Minas Gerais (Brazil), Oxford and Heriot-Watt (both in the UK), the University of Bucharest (Hungary) and ETH Zürich (Switzerland).
The programme itself was also highly international: the six mini-courses were delivered by highly prestigious researchers from around the world: “New equilibria in the Liquid Drop Model”, by Manuel del Pino (University of Bath, UK); “Non-local games: a link between mathematics, physics and computer science”, by David Perez (ICMAT-UCM); “Fourier and Schur multipliers”, by Javier Parcet (ICMAT-CSIC); “The ternary Goldbach Conjecture revisited”, by Harald Helfgott (Institut de Mathématiques de Jussieu, France); “Discrete Harmonic Functions”, by Eugenia Malinnikova (Stanford University, USA); and “Flows, periodic orbits and linking number”, by Ana Rechtman (University of Grenoble, France). Each of these courses provided an accessible introduction to important research areas, tailored for undergraduate students. “The standard of the lecturers is amazing—this year, for instance, we had Harald Helfgott, who proved the weak Goldbach conjecture,” said José Antonio Fuentes, participant in the 2025 JAE School and Severo Ochoa Intro Fellow, who recently completed his Mathematics degree at the University of Granada.
In addition, six more researchers delivered shorter talks that broadened the range of scientific topics covered: “Szemerédi’s Theorem turns 50”, by Pablo Candela (ICMAT-CSIC); “New methods in the theory of the Euler equations: Extrapolation and Sparseness”, by Óscar Domínguez (CUNEF); “Gravitating vortices and symplectic reduction by stages”, by Mario Garcia-Fernandez (ICMAT-CSIC); “Groups acting on trees”, by Alejandra Garrido (ICMAT-UCM); “How complicated can a group with a single defining relation really be?”, by Marco Linton (ICMAT-CSIC); and “From PDE to AI: mathematical journey”, by Clara Torres (ICMAT-CSIC). “I decided to take part in the JAE School because it’s a way to learn about areas of mathematics that aren’t covered in the undergraduate degree,” said Celia Coca, a student at the University of Granada, participant in the 2025 JAE School and Severo Ochoa Intro Fellow.
Participants were also able to share their questions and insights during a roundtable on research careers in mathematics, featuring Helfgott, Rechtman, José Antonio Lucas (ICMAT-CSIC) and Ana Bravo (ICMAT-UAM), moderated by ICMAT Director Javier Aramayona. The programme also included a professional development talk—“Developing a career in mathematical research”, delivered by Mónica Castresana (ICMAT-CSIC)—and a public outreach lecture, “Riddles and patterns of prime numbers. From Goldbach to twin primes”, by Harald Helfgott, held at the Residencia de Estudiantes.
The 2025 edition was organised by Diego Córdoba (ICMAT-CSIC) and Daniel Peralta-Salas (ICMAT-CSIC). Attendance, as always, was free of charge.
First steps in developing a research career in mathematics
Alongside the School, ICMAT also runs the 2025 Severo Ochoa Introductory Research Fellowships (INTRO-SO). Through this programme, 25 undergraduate students—and, exceptionally, Master’s students, who also attend the JAE School—undertake a one-month training placement (between 9 June and 31 July 2025), supervised by a researcher at ICMAT. They work on a topic of their choice from a list of proposed subjects. The aim of these fellowships is to introduce participants to some of ICMAT’s research lines and actively involve them in the Institute’s scientific activity.
“I chose to focus on partial differential equations because they appear in many areas of mathematics and, thanks to this fellowship, I was able to explore the topic in depth,” said Celia Coca, a student at the University of Granada and one of this year’s fellowship recipients. She is working on the inverse conductivity problem, supervised by María Ángeles García Ferrero (ICMAT-CSIC).
—