ICM 2026: “The plenary lectures help make mathematics accessible to all mathematicians”
From July 23 to 30, 2026, the International Congress of Mathematicians (ICM) will be held in Philadelphia, United States. Patrick Gérard will deliver a plenary lecture there, providing the mathematician with an opportunity to present his recent work in the theory of partial differential equations.
Every four years since 1897, mathematicians from around the world have gathered for the International Congress of Mathematicians. This event brings together researchers from all walks of life around a shared discipline. Patrick Gérard, a mathematician at the Orsay Institute of Mathematics1 , shares with us the importance he places on this event.
What makes this gathering of the mathematical community so special?
Patrick Gérard: The International Congress of Mathematicians (ICM) is an opportunity for mathematicians to come together, build connections, and form a single, unified community. This is not a given, as mathematics is organized into many subdisciplines. Thus, this event helps ensure that scientists can continue to use the same language to communicate, regardless of their fields or nationalities.
The ICM also serves to honor a number of researchers, among whom are generally four young mathematicians under the age of 40 who will be awarded the Fields Medal. This award recognizes early work or a body of promising early work.
What are the unique features of this edition, which will be held in Philadelphia from July 23 to 30?
As with every ICM, the fields represented will be very diverse. The goal of the congress is to maintain a sort of balance across the themes—and I believe the list of lectures reflects that well, in fact. This edition will, however, be somewhat unique due to the geopolitical situation. Indeed, some of our colleagues will be unable to obtain visas; other mathematicians have decided not to participate because the event is being held in the United States under the current circumstances.
What role does the French mathematical community play in this event?
Mathematics is a highly developed field in our country, and many French mathematicians are internationally recognized. A good indicator of the vitality of our mathematical community is the number of French speakers at this event. There are a significant number at each edition, given the size of our country. Of course, other countries have more impact or are gaining momentum, such as China in particular.
You are one of the invited speakers; you will be giving a plenary talk at the conference. What makes this presentation unique?
Plenary talks are a challenging task because they must be accessible to the entire community. The goal is to ensure that mathematics remains accessible to as many mathematicians as possible.
In just one hour, I have to make results accessible that took my colleagues and me months (or even years) of work to achieve. For example, I have to use as little of the jargon specific to my field as possible. It’s both very exciting and challenging!
Nevertheless, I think it’s wonderful that we still consider this exercise possible. We mathematicians rarely have the opportunity to attend a lecture on a specialty other than our own, even though in France, the Bourbaki Seminar also tries to maintain this unity within the community.
Alongside these plenary lectures, parallel sessions are also held that are aimed more at specialists in the various disciplines.
How are plenary speakers selected?
Several panels of mathematicians, kept secret until the end of the conference, meet two years before the start of the ICM. Each panel compiles a list of speakers for a specific area of mathematics based on recent work and by consulting other mathematicians. From this list, they propose one or two names as plenary speakers, who are ultimately selected by another committee. This results in about twenty plenary lectures.
Selecting these speakers involves a significant amount of work. The International Congress requires a massive organizational effort, which the mathematical community is capable of undertaking. I hope this will continue to be the case for many years to come.
How did you choose the topic for your presentation?
We have complete freedom in choosing the topic. In my case, the choice was easy: I will be presenting findings that are based on the scientific work I have recently carried out with my colleagues.
Could you tell us more? What are these results?
My specialty is the theory of partial differential equations—that is, equations in which the unknown is a function, and which often describe physical laws. In my field, we are often interested in how a system evolves over time (for example, the evolution of a wave on the open sea).
Generally, describing this evolution is difficult, especially over long time scales where numerical methods yield poor results. But sometimes, in the case of nonlinear equations, we can observe special solutions, called solitons, which always appear regardless of the initial conditions. In the case of waves over deep water, these special solutions resemble positive rational fractions moving at a constant speed. They were discovered in 1967 by the mathematician Thomas Brooke Benjamin (1928–1995).
Following this work and similar studies of other equations of the same type, the mathematical community formulated a general conjecture, known as the “soliton resolution,” according to which, over long time scales, the solutions to these equations will be superpositions of solitons traveling at distinct speeds, combined with a radiation term. Together with my two colleagues, Louise Gassot, a CNRS researcher at the Rennes Institute for Mathematical Research (IRMAR)2 , and Peter Miller, a professor at the University of Michigan, we have proven this conjecture in the case of the equation introduced by Benjamin. My presentation will focus on the proof of this result and on the new method we used.
You mention the colleagues you’ve worked with. How important are collaboration and discussion in mathematics?
Contrary to popular belief, mathematicians today very rarely work alone. Relationships form between mathematicians working on the same topic, and they may write a paper together. It’s a deeply rewarding human experience. When I received the invitation to participate, I immediately thought of those with whom I had collaborated, particularly Thomas Kappeler, who passed away suddenly four years ago. His work inspired me immensely and helped launch the research I’m currently conducting.
It is often at events such as the ICM that relationships or collaborations can form. Financial stakes in mathematics are fairly limited, so generally few people lay claim to the ideas we’ve shared. Discussions are free and relaxed. It is also this richness of collaboration that is celebrated at the International Congress of Mathematicians.