- From July 23 to 30, 2026, the International Congress of Mathematicians (ICM) will take place in Philadelphia (USA).
- Three members of ICMAT will participate: Javier Parcet (ICMAT-CSIC) and David Pérez García (ICMAT-UCM), who will deliver scientific lectures as invited speakers, and Ágata Timón (ICMAT-CSIC), who will take part in a roundtable on public communication of mathematics.
- The 2026 edition of the ICM will feature 12 Spanish mathematicians, an exceptionally high number that reflects the excellent period that mathematical research is experiencing in the country.
From left to right, Javier Parcet (ICMAT-CSIC), David Pérez García (ICMAT-UCM), and Ágata Timón (ICMAT-CSIC), participants in the 2026 International Congress of Mathematicians. Images: (1) Iñigo de Amescua/ICMAT, (2) provided by Pérez, and (3) provided by Timón.
Madrid, July 8, 2025. From July 23 to 30, 2026, the most important mathematical forum will be held in Philadelphia (USA): the International Congress of Mathematicians (ICM). Hundreds of specialists from all fields of the discipline will gather to share the most outstanding results of recent years. It is also the occasion on which the Fields Medals —the equivalent of the Nobel Prize in mathematics— are announced.
Yesterday, the ICM released its list of speakers, which includes three ICMAT members: Javier Parcet –Research Professor at the Spanish National Research Council (CSIC) at ICMAT– and David Pérez García –Professor at the Complutense University of Madrid (UCM) and ICMAT member–, who will be invited speakers in the Analysis and Mathematical Physics sections, respectively, and Ágata Timón –Coordinator of the ICMAT Mathematical Culture Unit–, who will participate in a roundtable on public communication of mathematics.
“Being named a speaker at the ICM is one of the greatest honors in our discipline. These invitations are a significant recognition of ICMAT’s scientific excellence, largely thanks to the support of the Ministry of Science, Innovation and Universities’ ‘Severo Ochoa and María de Maeztu’ Centers and Units of Excellence Program,” said Javier Aramayona, director of ICMAT.
This edition includes 12 Spanish participants, a notably high presence. In addition to Parcet, Pérez, and Timón, other participants are: Xavier Tolsa (Universitat Autònoma de Barcelona (UAB) and Centre de Recerca Matemàtica (CRM)) –giving a plenary lecture; David Aspero (University of East Anglia, UK), Xavier Cabre (Universitat Politècnica de Catalunya and CRM), Gabriel Navarro (University of Valencia), Joaquim Ortega Cerdá (University of Barcelona and CRM), Joaquín Pérez (University of Granada), and Enrique Zuazua (University of Erlangen-Nuremberg, Germany), who will give invited lectures in various sections; and Núria Planas (UAB) and M. Pilar Vélez (Universidad Nebrija), who will join roundtables.
“This wide participation from Spain at ICM 2026 highlights the strong momentum of mathematics in the country,” said Aramayona. Since the congress was founded in 1897, fewer than 20 Spanish mathematicians have participated as invited or plenary speakers in previous ICMs, showing the high standards of the event. Diego Córdoba, CSIC Research Professor at ICMAT, was the first ICMAT member to participate in the ICM, in 2018.
“Participation in the ICM is recognition of ICMAT’s commitment to scientific outreach. We conduct ongoing work to convey to society the importance, beauty, and value of mathematics,” added Aramayona.
These will be the topics addressed by ICMAT members at the 2026 International Congress of Mathematicians:
Unraveling Quantum Phases of Matter
“Quantum theory predicts numerous exotic phases of matter, going far beyond the classical solid, liquid, and gas,” explains David Pérez García, Professor at UCM and ICMAT member. Understanding and classifying these phases is currently one of the major challenges in mathematical physics. Mathematics is essential to tackle this.
The team led by Pérez García, co-directed with Ignacio Cirac at one of the ICMAT-Severo Ochoa Laboratories, has achieved significant results in this direction. “First, we showed that some problems are undecidable —they cannot be mathematically proved or disproved,” says Pérez. “Additionally, we developed the tensor network theory, a mathematical technique suited for analyzing quantum phases of matter. This has allowed us to estimate the lifetime of quantum memories or even provide privacy guarantees in machine learning processes,” he describes. These advances will be the subject of his invited lecture in the Mathematical Physics section.
Progress on Connes’ Rigidity Conjecture
The shape of a drum, its depth, or the tension of its membrane affects its sound. But from its sound, can one deduce its shape? Based on this classic analogy from harmonic analysis, more complex structures can be studied through the tones they produce. This offers a promising approach to shedding light on the so-called Connes’ rigidity conjecture —one of the most important open problems in functional analysis and geometric group theory. The rigidity conjecture, proposed in 1980, predicts the non-equivalence of certain von Neumann algebras —structures that rigorously formalize Heisenberg’s matrix mechanics in quantum physics— associated with highly complex groups, such as high-rank semisimple lattices.
Returning to the analogy, “each von Neumann algebra admits, in a certain sense, a specific range of tones. We aim to clarify these acoustic ranges using tools from harmonic analysis —namely, Fourier and Schur multipliers— to conclude that these structures are not equivalent and thereby prove the conjecture or at least shed light on it,” explains Javier Parcet. A CSIC Research Professor at ICMAT and co-director of another ICMAT Severo Ochoa Laboratory, Parcet has developed new inequalities for Schur multipliers that extend deep results in late 20th-century harmonic analysis. “These inequalities are particularly versatile due to the flexibility of Schur multipliers, in contrast to their Fourier counterparts in classical harmonic analysis,” adds the mathematician. He will present these topics in his invited lecture in the Analysis section.
A Commitment to Mathematical Culture
In 2012, ICMAT became one of the first mathematics centers to have a permanent press office. Beyond media relations, the ICMAT Mathematical Culture Unit organizes diverse activities to bring mathematics to non-specialist audiences: workshops, lectures, books, theater plays… Ágata Timón has coordinated the unit since its inception and, with her extensive experience, has become a reference in public communication of mathematics. She will discuss this work in the roundtable Communicating Mathematics in (Physical & Virtual) Public Spaces.
Javier Parcet Javier Parcet’s research stems from a broad conception of harmonic analysis, with connections to geometric group theory, quantum probability, operator algebras and spaces, and metric geometry. He earned his PhD in Mathematics from the Universidad Autónoma de Madrid in 2003 and joined ICMAT in 2006 under a Ramón y Cajal contract, following postdoctoral stays at Texas A&M University, Urbana-Champaign, and CRM Barcelona. He is currently a CSIC Research Professor, leads a highly recognized research group, co-directs the Pisier / de la Salle Laboratory at ICMAT, and is an editor of the Journal of Functional Analysis and Revista Matemática Iberoamericana. Among other honors, he received the José Luis Rubio de Francia Prize —Spain’s most prestigious award for young mathematicians— in 2006, and one of the prestigious ERC Starting Grants (2010–2015) to develop noncommutative Calderón-Zygmund theory. David Pérez García Pérez García specializes in the application of mathematics to quantum information theory. He co-leads the Ignacio Cirac Laboratory at ICMAT and heads the Quantum Information and Mathematics group at UCM. He earned his Mathematics degree from UCM in 2000 and his PhD in 2004. He then held postdoctoral positions at the Max Planck Institute in Germany and at UCM, where he was a Ramón y Cajal researcher. His distinctions include an ERC Consolidator Grant (2015), the Royal Academy of Sciences Endesa Prize in Mathematics (for researchers under 40) in 2013, the John von Neumann Guest Professorship at the Technical University of Munich in 2014, the Miguel Catalán Award for outstanding researchers under 40 from the Madrid regional government in 2017, the 3rd Fundación Banco Sabadell Prize for Science and Engineering in 2019, and the Ramón y Cajal Medal (2021). Since 2023, he has been a Full Member of the Royal Academy of Sciences. Ágata Timón Ágata Timón García-Longoria has coordinated the ICMAT Mathematical Culture Unit since its creation in 2012. She holds a degree in Mathematics from the Complutense University of Madrid and master’s degrees in Science Journalism and Communication, and Applied Research in Media, both from the Carlos III University of Madrid. Timón has focused her career on disseminating mathematics in various formats —primarily writing, but also video, audio, and live events such as workshops, lectures, and theater plays. She is the author of five science outreach books. Since 2016, she has coordinated the math section Café y Teoremas in *El País*, the most prominent Spanish-language newspaper, and has published over 250 articles on science, particularly mathematics. She has also taught at Universidad Nebrija and has been a speaker at several science communication courses.
The World’s Largest Mathematics Forum The ICM has been held every four years since 1897 and is considered the most important mathematical event in the world. Over seven days, plenary and invited lectures are delivered on topics ranging from pure mathematics —such as algebra, topology, and number theory— to others related to different fields of knowledge, such as mathematical physics, computing, education, outreach, and the history of mathematics.
This is an automatic translation. Differences from the original Spanish text may exist.