IHES Trust UK, the UK charity partner of IHES, was officially launched at the Residence of France in London on the 12th of June. The event took place under the esteemed patronage of H.E. Hélène Duchêne, Ambassador of France to the United Kingdom, and in the presence of Sébastien Bidaud, Minister-Counsellor at the French Embassy in the United Kingdom, along with around one hundred IHES ambassadors in the UK and science enthusiasts. This event was organized with the support of XTX Markets, a longstanding donor to IHES.

Francis Brown, Professor of Mathematics at Oxford University and Chair of the Board of Trustees of IHES Trust UK, took the opportunity to introduce the charity’s board of trustees, which includes Guillaume Bioche, Rama Cont, Amy Gibson, and Clotilde Walewska. He also expressed his gratitude to the charity’s future supporters for their commitment to science and reaffirmed the mission of the organization.

On this occasion, Sir Timothy Gowers, holder of the Combinatorics Chair at the Collège de France, Professor of Mathematics at the University of Cambridge, and Fields Medal laureate, delivered a talk entitled The Impact of AI on Mathematical Research. His presentation sparked animated discussions on a topic of growing interest within the mathematical community.

Guests of this special event enjoyed a reception in the gardens of the Residence, providing an opportunity to meet and connect in a unique setting. This launch event marks the beginning of what promises to be a fruitful tradition of scientific events hosted by IHES Trust UK.

From left to right: Amy Gibson, Clotilde Walewska, Guillaume Bioche, Sébastien Bidaud, Rama Cont, Emmanuel Ullmo (Director of IHES), Francis Brown, Timothy Gowers, Jean-Pierre Bourguignon (former Director of IHES).

New event organised by Les Amis de l’IHES on Wednesday 18 June 2025, 5:30 pm (French time) at IHES.

Elsa VENNAT, (CentraleSupélec) gave an hybrid conference in French entitled:

“Odyssey into the heart of teeth, at the boundary between biology and materials science,
to understand tissues and their pathologies.”

Why is it better to run behind someone? Biological tissues such as bones and teeth are extraordinary materials.
Mechanically, they are highly efficient, whereas their basic constituents are much less so.
Why is it so? Because they are structured on several levels.What’s more, these tissues perform multiple functions and are constantly evolving.For example, bone tissue adapts to the stresses it undergoes thanks to sensitive cells!
Teeth, on the other hand, evolve but do not regenerate naturally, unlike bones. Nevertheless, cells similar to those of bone tissue have produced them:How are teeth formed? How are dental tissues formed? How do tissues react to externalaggressions? How does biology affect the structure and properties of teeth in diseases
such as the “brittle bone disease”?

The conference will be followed by a musical interlude with Alexandra KORTCHEMSKI (piano) in the foyer of the Centre de conférences Marilyn et James Simons.

Please note: exceptionally, in-person registrations will be limited to 40 people.

Contact: Ingrid Peeters

IHES is pleased to announce that Henri Seydoux, founder and CEO of Parrot, will chair its fourth capital campaign, set to launch at AXA’s Paris headquarters on December 2, 2025.

Henri Seydoux’s deep interest in science—and in particular, mathematics and theoretical physics—led him to discover IHES through the archives of Alexandre Grothendieck, Fields Medalist, Permanent Professor at IHES from 1958 to 1970, and a towering figure in the Institute’s history.

His first donation to IHES supported the publication of Récoltes et semailles, Grothendieck’s seminal autobiography, published by Gallimard in 2022. Since then, he has become a regular supporter of the Institute. Demonstrating his continued commitment, Henri Seydoux has pledged an exceptional €1,000,000 to launch this new campaign.

Through this major donation, Henri Seydoux aims to create a momentum to launch IHES’s fourth capital campaign. His personal commitment as Chairman of the Campaign Committee is also a strong testament to his confidence in and support for the Institute’s mission. Henri Seydoux explains: “Freedom of research—which safeguards the independence and objectivity of scientists—is increasingly being challenged, even in countries renowned for their academic excellence. The growing mistrust of science and the spread of misinformation are deeply concerning. I believe it is more important than ever to defend the model of free, curiosity-driven research of IHES.”

Emmanuel Ullmo, Director of IHES, adds: “We are deeply honoured to count on the support of Henri Seydoux, who, beyond his exceptionally generous financial contribution, offers his time, expertise, and network to the Institute. We are especially grateful to him for agreeing to chair this new campaign.”

A pioneer in fundraising for higher education and research in France, IHES increasingly depends on philanthropy to support its annual budget, which amounts to approximately €10 million. Whereas subsidies from the French Ministry of Higher Education and Research once covered the majority of the Institute’s funding, they now account for less than a third. As a result, the support of private donors—whether companies, foundations, or individuals—has become essential to sustaining the Institute’s activities and mission.

Since the late 1990s, and under the leadership of Jean-Pierre Bourguignon —Director of IHES from 1994 to 2013 and now Honorary Professor Nicolaas Kuiper—the Institute has turned to fundraising campaigns to help support its operations. These initiatives are led by committees composed of prominent figures from academia, finance, and industry. By chairing this fourth capital campaign, Henri Seydoux follows in the footsteps of distinguished individuals who have championed IHES, including Raymond Barre, Jean-Laurent Bonnafé, Philippe Camus, Anne Lauvergeon, André Lévy-Lang, Jim Simons and Jean-Claude Trichet.

New event organized by Les Amis de l’IHES on Wednesday April 9th, 2025 at 5:30 pm (French Time) at IHES

Andrea ZOIA (CEA) gave a conference in French in hybrid format, entitled:

«The Chicago Piles, a scientific adventure that changed the world »

What happened on December 2, 1942, under the bleachers of the University of Chicago’s Stagg Field stadium forever marked the history of mankind: by removing the last control bar and thus starting the “Chicago Pile”, Enrico FERMI and his colleagues demonstrated the feasibility of a controlled chain reaction. Thus they gave birth to the “nuclear age” of energy, just four years after the discovery of fission (December 1938). The vision of these pioneers had a lasting impacton the development of nuclear reactor technologies.

Registration

Zoom link to the conference:

https://us02web.zoom.us/j/82899632386?pwd=y8ITyDbPEXYhOLVSF8Tsad3CiXXc7r.1

Contact : Ingrid Peeters

New event organized by Les Amis de l’IHES on Tuesday January 21st, 2025 at 5:30 pm (French Time) at IHES

Cécile MICHEL Research Director at CNRS and Professor at Hamburg University, gave a conference (in French) in hybrid format, entitled:

“The origins of writing:
what can we learn from cuneiform writing?”

Cuneiform writing – in the shape of wedges – was the first form
of writing invented in the history of mankind around 3400 BC by the
Sumerians in Mesopotamia. It was used for almost 3500 years to transcribe
a dozen languages using different systems, proving to be extremely flexible.
Nearly a million cuneiform texts have been discovered since the mid-19th
century, thanks to the excellent preservation capacity of clay tablets.

Cécile Michel, an assyriologist at the CNRS, has built up a vast knowledge of this script.

This presentation was followed by a musical moment with Alexandra Kortchemski who performed works by Bach and Chopin.

Contact: Ingrid Peeters (01 60 92 66 64)

In 2012, French filmmaker Olivier Peyon traveled to the United States to film scenes for his documentary “Comment j’ai détesté les maths”, which explores mathematics and its cultural impact on society.

During his visit to New York, he conducted extensive interviews with Jim Simons, who also appears in the film. Following Jim’s passing in May, Olivier Peyon generously shared the rushes of his footage. The resulting video features Jim reflecting lucidly on his life as a mathematician, investor, and philanthropist.

He notably discusses his pioneering work on what would later become known as Chern-Simons theory, his entry into investing and the creation of Renaissance Technologies, and the beginnings of his philanthropic efforts, including the founding of the Simons Center for Geometry and Physics at Stony Brook.

IHES extends its deepest gratitude to Olivier Peyon for providing this moving homage to Jim.

Additional personal tributes to Jim by IHES affiliates can be found here.

The Institute is thrilled to announce a generous gift of $200k to the Friends of IHES Endowment Fund by its long-time supporters Mike and Nina Douglas. This gift, which will be matched by the Simons Foundation International, represents a major step in fostering mathematical and scientific collaboration across borders, as championed by IHES.

The annual proceeds from this donation will fund visits to IHES by mathematicians and physicists from Southeastern Europe (Albania, Bosnia and Herzegovina, Bulgaria, Croatia, Greece, North Macedonia, Montenegro, Romania, Serbia, Slovenia). A special invitation is also extended to theoretical computer scientists working on the mathematical foundations, and the use of artificial intelligence in mathematics—a rapidly growing field of global importance and one of Mike Douglas’s own research interests. Mike notably organized a conference titled Mathematics for and by Large Language Models at IHES in May 2023.

The ties of the Douglas family to Southeastern Europe run deep. Nina is of Bulgarian origin and had a Greek grandmother with whom she shared a very close relationship. Additionally, Mike’s father, mathematician Ronald G. Douglas, had strong ties to the Romanian mathematical community, working with Constantin G. Apostol, Ciprian Foiaș, and Dan-Virgil Voiculescu on operator theory and operator algebras.

The Douglas family’s relationship with IHES is equally profound. Mike Douglas, a pioneer in string theory and mathematical physics, was a Professor of Physics at Rutgers University and Stony Brook University, was a founding member of the Simons Center for Geometry and Physics, and is currently a Senior Research Scientist at Harvard University. He was the holder of the Louis Michel Chair at IHES from 2000 to 2011. During this time, he and Nina became integral members of the IHES community. Together, they have fond memories of raising their children at the Ormaille residence of the Institute. Mike also served as President and Chairman of Friends of IHES from 2013 to 2021, playing a pivotal role in strengthening ties between the Institute and its community of supporters in the United States.

Nina, a mathematical linguist with a PhD in philosophy and comparative literature, is also an artist whose creations often draw from the realms of mathematics and physics. Her bronze sculpture of Alexander Grothendieck, gifted to IHES by Marilyn and Jim Simons in 2014, is now permanently displayed in the Alix and Marwan Lahoud Building at the Institute.

The vision of the Mike and Nina Douglas visitor program closely aligns with the broader mission of IHES to cultivate global scientific exchange. Yuri Tschinkel, Executive Vice President of Mathematics and Physical Sciences at the Simons Foundation and a member of the IHES Board of Directors, emphasized the significance of this initiative, stating:

“I visited the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences in 2022 and was deeply impressed by the level of mathematics being done there. I am delighted to hear that more aspiring mathematicians from Southeastern Europe will be able to connect with leaders in their fields at IHES.”

This major gift marks not only a continuation of the Douglas family’s enduring commitment to IHES but also a powerful investment in the future of mathematical and scientific talent from Southeastern Europe. It is a testament to the transformative power of philanthropy and the global reach of IHES as a hub for pioneering research and international cooperation.

Applications for the Southeastern Europe visitor program will open in the Fall of 2025 for visits to IHES starting in 2026.

Yilin Wang, Junior Professor of Mathematics at IHES, has been awarded the 2024 Salem Prize.

The Salem Prize, administered by the Institute for Advanced Study in Princeton, is awarded annually to a young mathematician who has made outstanding contributions to harmonic analysis and related fields. Named after the French mathematician Raphaël Salem, the prize honors his legacy as one of the great analysts of the 20th century.

Wang was awarded the Salem Prize for her “development of deep, novel connections between complex analysis, probability, and mathematical physics, particularly in relation to Teichmüller theory and Schramm-Loewner evolution.”

“Yilin Wang has uncovered many new features and approaches to study the Schramm-Loewner evolution that drives many important random structures in the complex plane. I personally look forward to seeing where her work takes the subject in the future,” says Terence Tao, Chair of the Scientific Committee of the 2024 Salem Prize.

In her doctoral thesis, Yilin Wang introduced a concept called the Loewner energy to quantify the roundness of simple planar curves. Intuitively, the Loewner energy measures the extent to which a curve deviates from being a perfect circle. Wang used this concept to study a unique class of random planar curves, known as Schramm-Loewner evolution (SLE), which model interfaces in 2D critical lattice models and conformal field theory (CFT).

The introduction of the Loewner energy enabled Wang to bridge SLE with Teichmüller theory and hyperbolic geometry. In particular, she discovered that the action of the SLE loop measure coincides with the Kähler potential of the universal Teichmüller space—an infinite-dimensional complex manifold that includes Teichmüller spaces of Riemann surfaces as complex submanifolds—where the study of the Kähler structure was first motivated by string theory. In collaboration with Fredrik Viklund, she worked on proving new results on the universal Teichmüller space inspired by results on SLEs and, more broadly, random conformal geometry.

“When Yilin’s first paper landed on my desk, I was immediately excited by it and quickly began exploring questions around the Loewner energy. Later, at a workshop, she explained her newly discovered links between the SLE world (which I knew well) and new areas for me, such as Teichmüller theory. These connections were strikingly beautiful, intriguing, and even mysterious. I knew this was a direction I wanted to pursue,” recalls Fredrik Viklund.

“We started an intense and productive collaboration. The first paper came together quickly, but the second required much harder work. Guided by her strong aesthetic sense, Yilin pushed us to achieve not only optimal results but also the most elegant proofs. In the end, our work paid off, resulting in what is perhaps my most satisfying paper,” Viklund adds.

In a recent preprint with Martin Bridgeman, Kenneth Bromberg, and Franco Vargas Pallete, who is currently a postdoctoral researcher at IHES, Wang and her co-authors were able to link the Loewner energy to the renormalized volume of hyperbolic 3-manifolds. This connection suggests a holographic principle for the Loewner energy, reminiscent of the conjectured $AdS_3/CFT_2$ correspondence in string theory, proposed by Juan Martín Maldacena.

Looking ahead, Yilin Wang aims to establish a broader holographic correspondence in the context of random conformal geometry using the probabilistic approach to conformal field theory.

“Congratulations to Yilin Wang for receiving the 2024 Salem Prize. Besides producing excellent research, Yilin Wang is a very active member of the Institute, and a driving force of the scientific activity at IHES. She perfectly embodies the cooperative and interdisciplinary spirit that we cultivate at IHES,” concludes Emmanuel Ullmo, Director of IHES.

Photo credit : Chris Peus / IHES

Celebrating IHES’ Visionary Scientists (page 3) :

 

Recordings of the conference in honor of René Thom

Recordings of the conference in honor of Yvonne Choquet-Bruhat

Remembering Einstein’s Groundbreaking Contributions to Science (a video featuring Thibault Damour)

Alexandre Grothendieck, légende rebelle des mathématiques (Podcast on Alexandre Grothendieck in French)

‘He was in mystic delirium’: was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman? (Article in The Guardian on Alexandre Grothendieck)

 

New Arrivals in Physics (pages 4 & 5) :

 

Clément Delcamp, Junior Professor of Physics

Recordings of Clément Delcamp’s Cours de l’IHES on Topological Symmetry and Duality in Quantum Lattice Models

Introducing Julio Parra-Martinez, new Permanent Professor of Physics

Recordings of the IHES Summer School Symmetries and Anomalies: a modern take

 

Scientific Life (pages 6 & 7) :

 

In Memoriam: Nicolas Bergeron (1975-2024)

In Memoriam: Pierre Cartier (1932-2024)

In Memoriam: Henri Epstein (1932-2024)

 

Tribute to Jim Simons (pages 8 & 9) :

 

In Memoriam: Jim Simons (1938-2024)

 

Scientific Events (pages 10 & 11) :

 

Recordings of the 9th Statistics & Computer Science Day for Data Science in Paris-Saclay

Recordings of the Mathematics for and by Large Language Models conference

Recordings of the Physical Mathematics: Celebration of Albert Schwarz’s 70 Years in Science conference

Recordings of Albert Schwarz’s Cours de l’IHES on Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Recordings of Dustin Clausen’s and Peter Scholze’s Cours de l’IHES on Analytic Stacks

Recordings of the Arithmetic Geometry conference in honor of Hélène Esnault

Interviews with Maxim Kontsevich and Yilin Wang by CNRS in relation with their plenary and invited talks at the European Congress of Mathematics in Seville

 

Exploring Mathematics (page 12) :

 

Dennis Gaitsgory on the Geometric Langlands Correspondence

 

Outreach (page 14) :

 

Looking back at the conference by Catherine Goldstein and Clémence Perronnet

Annual High School Students’ Visit to the Institute

Hugo Duminil-Copin, Event Ambassador for the International Mathematical and Logical Games Championship

Recording of the public lecture Blaise Pascal, la mathématique au cœur de l’humanité by Cédric Villani (in French) 

Recording of the public lecture La science au service de la performance des sportifs by Amandine Aftalion (in French)

 

Fundraising and Development (page 15) :

 

Record-breaking 2023 Gala on Jazz and Physics

IHES in New York City

IHES in Singapore

Inaugural Ceremony of the Jean-Pierre Bourguignon Chair

 

Point of View (page 16) :

 

Veronica Fantini’s personal website

Recordings of the workshop on Quantum Geometry

Recordings of the mini-course New Perspectives on Borel Summation

Website of the Quantum modularity and resurgence Seminar

This is an account of Jim Simons’ return to mathematics in the early 2000’s.

There is a “first indication” story:
After Jim left research per se in the late 1970’s, there was a math discussion at his 60th birthday fest in 1998 at Stony Brook, where Jim revealed to Maxim Kontsevich and me that he had been wondering about the meaning of two connections having (pointwise) the same invariant polynomials built on the curvature. He mentioned especially the case where one connection is flat.

I recall being shocked that this question made good sense and that, to my knowledge, no one had thought to ask it before.

A second stimulus:
This was Blaine Lawson’s preprint for the published paper The de Rham-Federer Theory of Differential Characters and Character Duality, giving a completely different geometric and analytic construction of the receptacle “differential characters” for the first Jim Simons’ invariant of 3-manifolds (this receptacle having been constructed by Jim with Jeff Cheeger in the early 1970s. This was contemporary with Pierre Deligne’s construction of Deligne Cohomology in algebraic geometry which transposed into differential geometry seemed equivalent to the Cheeger-Simons receptacle or theory called “differential characters”).

Jim had the idea to axiomatize such theories that resulted in the paper Axiomatic Characterization of Ordinary Differential Cohomology. These equivalent versions of differential characters being renamed there “Ordinary Differential Cohomology” because a seminal paper, Quadratic Functions in Geometry, Topology, and M-Theory, by Mike Hopkins and Isadore Singer defined a general construction for every “extraordinary cohomology theory”, for example complex K-theory, now referred to as differential K-theory.

This was the beginning of a dozen year mathematical collaboration of Jim with me that tied the above two stories together with a still unfinished story about a question raised by Isadore Singer which was motivated by theoretical physics. This being connected with the fact that the higher dimensional Chern-Simons versions of Jim’s first invariant of 3-manifolds (called “Chern-Simons terms”) are used frequently up to the present day in theoretical physics papers.

There were several papers [3-7] in this collaboration with Jim which were likely related to his being elected to the National Academy of Sciences (NAS) in 2014, because they showed Jim was still a true scientist besides being a great supporter of science.

I recall a gala dinner for the National Museum of Mathematics where Jim was introduced mentioning an article in the New York Times about his election to the NAS entitled “The world’s smartest billionaire”. As Jim walked to the podium, I wondered how he would react.

He was perfect. He said “How many billionaires are there in the world? I would rather be the world’s smartest millionaire!”. We all laughed and relaxed. It was Jim Simons at his best!

Regarding his support of science as compared to being a scientist, it has not been mentioned enough that Jim usually did much more than providing financial support for projects related to science and to other worthy endeavors in which he was involved.

Besides contributing capital, Jim worked hard day to day to ensure the health and success of these projects. In the case of the Simons Center for Geometry and Physics, I noted that he attended every meeting related to its design, its evolution and its maintenance until the very end of his capabilities.

He worked very hard all the time. I once guessed it might be about three times the normal busy schedule of a hard-working person.

Dennis Sullivan
New York, October 2024

References

[0] S.-S. Chern, J. Simons: Characteristic Forms and Geometric Invariants. Annals of Mathematics, Vol. 99, No. 1 (Jan., 1974), pp. 48-69

[1] B. Lawson, R. Harvey and J. Zweck: The de Rham-Federer Theory of Differential Characters and Character Duality. American Journal of Mathematics 125, No. 4, 791—847 (2003)

[2] M. J. Hopkins and I. M. Singer: Quadratic Functions in Geometry, Topology, and M-theory. J. Differ. Geom. 70, No. 3, 329—452 (2005)

[3] J. Simons and D. Sullivan: Axiomatic Characterization of Ordinary Differential Cohomology. J. Topol. 1, No. 1, 45—56 (2008)

[4] J. Simons and D. Sullivan: The Atiyah Singer Index Theorem and Chern Weil Forms. Pure Appl. Math. Q. 6, No. 2, 643—645 (2010)

[5] J. Simons and D. Sullivan: Structured Vector Bundles Define Differential K-theory. Clay Math. Proc. 11, 579—599 (2010)

[7] J. Simons and D. Sullivan: Differential Characters for K-theory. Prog. Math. 297, 353—361 (2012)

[7] J. Simons and D. Sullivan: Characters for Complex Bundles and their Connections. arXiv:1803.07129 (2018)
(containing an Appendix with a remarkable calculation/determination by Jim related to the adiabatic limit of certain distinct connections becoming “Chern-Simons” equivalent.)

 

From left to right: Louis Michel, Oscar Lanford, Henri Epstein, and Marcel Berger.

I remember Henri Epstein as a fun and helpful colleague.

When Michael Herman was lecturing on his work on the conjugacy of diffeomorphisms of the circle to rotations, Henri and I often walked across the valley together to attend his talks. Even though Michael’s lectures were highly technical, Henri persisted, showing his incredible tenacity in rigorously understanding every aspect of a mathematical proof.

Let me now tell you about how Henri helped me with a mathematics problem related to period doubling universality.

Henri showed that there is a real-analytic solution to Feigenbaum’s functional equation:

$$g \circ g(\lambda x) + \lambda g(x) = 0,$$

where $g: [-1, 1] \rightarrow [-1, 1]$ is an even function such that $g(0) = 1.$

He observed that the solution to this functional equation had inverse branches for which there exist complex analytic extensions to the entire upper half-plane. He also created computer-generated images of the complex fixed point of renormalization.

These real-analytic functions with complex analytic extensions arose naturally in my own eight-year struggle with period doubling universality, and I thus named these functions “functions in the Epstein Class.”

There are still many open questions regarding one-hump mappings of the line, particularly about the power used to shape the hump. Numerical experiments by physicists suggest that there is a universal geometry for each real power greater than one, but this is unproven except for even powers. In the case of even powers, the proof relies on complex analytic extensions of the forward mapping.

The argument shows that the backward branches, for any real power, have real-analytic renormalization limits within the Epstein Class. I believe this fact will play an important role in any future proof of this true, yet unproven, theorem.

Let me finish with another story involving Henri, related to the final stage of my struggle with period doubling universality.

By 1989, I was two-thirds of the way through proving the universality of the differentiable structure on the critical orbit Cantor set, defined by the infinite period doubling cascade. However, I still needed the complex bounds on these complex analytic extensions, and they were simply not forthcoming.

Bill Thurston was a huge presence in geometry at the time, and in my desperation, I decided to imitate him by “drawing pictures and using visual thinking” in a last attempt to establish the necessary bounds.

Here’s how my reasoning went:

The square root of the upper half-plane is a quarter-plane. Translate this to the right, take the square root again, and you get something with two right angles derived from the quarter-plane. Repeat this process over and over again, and you’ll end up with a fascinating image—very much in the spirit of Thurston.

I drew this on the blackboard in the visitor’s room, downstairs from Henri’s office on the second floor.

Suddenly, I remembered that some time back, Henri had produced the computer-generated images of the complex fixed point of renormalization mentioned above—specifically, iterations of the backward branches.

I ran upstairs to Henri’s office, but no one was there. The door, though closed, wasn’t locked—quite common at IHES in those days. Through the window, I saw a shelf with his reprints. I charged in, found the relevant paper, and flipped to the page with the figure showing the complex fixed-point Henri had discovered with the computer.

To my amazement, the figure looked exactly like the one I had just drawn on the blackboard downstairs.

This gave us both a clear picture and a precise conjecture to prove about the necessary bounds.

It still took me months to finish the proof. The final step was completed in July 1990 at the Orsay pool with Wellington de Melo. I later presented the proof at the Orsay dynamics seminar, and within a few weeks, Marguerite Flexor wrote up a rigorous account of my lectures.

Thank you, Henri, and rest easy,

Dennis Sullivan
New York, October 2024