The award ceremony of the International Union of Mathematicians held on July 5 in Helsinki honored several mathematicians who have, at some point or another, been related to the Institute.

The Fields Medal is considered the world’s most prestigious award in mathematics and is awarded every four years at the International Congress of Mathematicians. The four winners of this year’s Fields Medal announced today are Hugo Duminil-Copin, permanent professor at IHES and professor at the University of Geneva, Maryna Viazovska, professor at the Ecole Polytechnique Fédérale de Lausanne, June Huh, Professor at Princeton University, and James Maynard, Professor at the University of Oxford.

Ukrainian mathematician Maryna Viazovska, a full professor at EPFL, where she holds the Chair of Arithmetic, was a post-doctoral researcher at IHES between 2012 and 2013. She also gave a series of six Hadamard lectures on automorphic forms and optimization in Euclidean space, organized by the Fondation Mathématique Jacques Hadamard at IHES in 2019. Prof. Viazovska solved the problem of compact packing of spheres in dimensions 8 and 24.

During the ceremony, other important prizes were awarded to scientists very close to the Institute. Most notably, Barry Mazur, Gerhard Gade University Professor at Harvard University, was awarded the Chern Medal, given every four years “to an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics”. Barry Mazur’s close relationship with IHES dates back to 1962, when the Institute had just moved to Bois-Marie, in the South of Paris. His research interests include number theory and algebraic geometry. His profound contributions to these subjects have earned him many awards, and this medal is the culmination of a lifetime’s work.

Other scientists from the Institute were also honored at the International Conference held online on July 6-14. Laure Saint-Raymond, a tenured professor at IHES, and this year’s ICM plenary speaker, addressed the dynamics of dilute gases in her lecture on Saturday, July 9.
Ofer Gabber, CNRS research director at IHES, was an invited speaker and gave a talk entitled “Bounding the torsion in the l-adic cohomology of smooth projective varieties without unbounded searches” on Monday, July 11.

IHES warmly congratulates these mathematicians on these prestigious awards, which testify to the profound impact of their research.

In this video, Nathalie Ayi and Laure Saint-Raymond discuss their view of mathematics and of research as a collective effort, and stress the importance of communication in making science widely accessible.

Laure Saint-Raymond is a permanent professor at IHES, Laboratoire Alexander Grothendieck (CNRS/IHES), Nathalie Ayi is an assistant professor at Sorbonne Université, Laboratoire Jacques-Louis Lions (CNRS/Sorbonne Université/Université de Paris).

This conversation was recorded in January 2022, in preparation to the 2022 International Congress of Mathematicians, where Laure Saint-Raymond will be a plenary speaker.

Professor Laure Saint Raymond joined IHES last September. Her work mainly focuses on the asymptotic analysis of partial differential equations, particularly those governing gas, plasma, and fluid dynamics. Notably, she made important contributions towards solving Hilbert’s sixth problem, at the heart of which lies Boltzmann’s equation.

This video, produced by Philip Yam for the Simons Foundation, explains the essence of Ludwig Boltzmann’s work and its relation to Hilbert’s challenge, as well as to Laure Saint-Raymond’s work.

IHES: You are starting a new stage in your career as a mathematician. How do you feel about it?

Laure Saint-Raymond: I can’t deny that I’m experiencing a twinge of sadness, as I leave the ENS de Lyon where I have spent five wonderful years. I enjoyed the dynamism of the mathematics laboratory, which is always at the forefront of its scientific development and its community commitments (dissemination and awareness of research, open publications, reduction of the carbon footprint, etc.). I also greatly appreciated the straightforward and exciting collaborations with the physics laboratory as well as the wealth and strength of the research network in Auvergne-Rhône-Alpes. I will maintain a small presence  there to continue to work on geophysical fluids and environmental issues, especially with the Institut des mathématiques de la Planète Terre.

Of course, I am also somewhat awestruck to be joining IHES, this prestigious institution which for the moment is more of a myth than a natural place in which to do my research. On the one hand, the list of permanent professors who have worked here sets the bar very high in terms of the depth and impact of their work. But on the other hand, the themes that have been developed here so far are quite foreign to me. In my mind, IHES refers to great names in mathematics that I don’t necessarily associate with faces, or to works that have revolutionized whole areas of the discipline but that I essentially don’t understand… It’s hard to identify something I can latch on to.

A blank page… perhaps that’s what really stimulates me! At the same time, this move represents great freedom, and the responsibility of making a new dynamic emerge, to make its own mark. I realize how lucky I am, even if it sometimes feels quite dizzying. IHES provides a very positive atmosphere for individual research work, while offering many opportunities to bring in foreign students or colleagues. Its scientific environment is extremely promising, bringing together the university in Orsay and the institutions and research centers in the Saclay area. I have no doubt that this mixture of calm and bustle will lead to unexpected encounters and will raise fruitful questions.

How would you describe your approach to mathematics?

I have neither the technical strength nor the will to tackle head-on the difficult conjectures to which some mathematicians devote their entire lives in a long arm-wrestling match. I prefer the side roads, the curiosities of physics, the surprising connections between apparently distant disciplinary fields… I like mathematics that formalizes simple intuitions, that can be shared.

In a way, mathematics is at the confluence of scientific reasoning and artistic creation. Not all mathematicians have the same tastes, but they attach importance to the notion of beauty. This is what I hope to be able to pass on to my students and more widely to the people I meet at events aimed at the general public.

One can try to convince people of the usefulness of mathematics, but that can be a slippery slope. However, one can without moderation marvel at all the ideas that slowly take seed and end up blooming where one did not necessarily expect them, at all the scattered abstract constructions that end up being strongly connected.

This magic of mathematics must make people dream… beyond the circle of mathematicians!

Laure Saint-Raymond’s homepage

The conference was held at IHES depending on the evolution of health situations and related restrictions.

The conference “Large-scale Limits of Interacting Particle Systems”, took place in the Marilyn and James Simons Conference Center from October 4 to 8 2021, and simultaneously on Zoom.

It was organized by Mitia Duerinckx (CNRS), Sergio Simonella (CNRS) and Raphael Winter (École Normale Supérieure de Lyon), with the support of the CNRS-Momentum program.

These five days brought together researchers interested in rigorous methods for the study of scaling limits of interacting particle systems.

The conference focused on three mini-courses, given by:

• Mathieu Lewin (CNRS): “Mean-field Limits and Bose-Einstein Condensation for Quantum Gases“;
• Laure Saint-Raymond (IHES): “Statistical Description of a Hard Sphere Gas Dynamics“;
• Manfred Salmhofer (Institute for Theoretical Physics, Univ. of Heidelberg): “Diagrammatic Expansions and Renormalization in Quantum Dynamics”

The program also included one-hour talks given by:

• Serena Cenatiempo (GSSI),
• Charles Collot (Cergy Paris Université),
• Sabine Jansen (LMU),
• Jens Marklof (University of Bristol),
• Alessia Nota (Università degli Studi dell’Aquila),
• Peter Pickl (University of Munich),
• Marcello Porta (SISSA),
• Mario Pulvirenti (Università di Roma « La Sapienza »),
• Nicolas Rougerie (UMPA),
• Florian Theil (University of Warwick),
• Bálint Tóth (University of Bristol).

To get more information on the conference program, and be informed of the latest measures taken, go to the dedicated web page.

Find all the videos of the conference: