Five-year Anniversary of the Gretchen and Barry Mazur Chair

2024 marks the five-year anniversary of the Gretchen and Barry Mazur Chair. This Chair, reserved for a mathematician visiting IHES, is endowed by gifts from Margaret and William R. Hearst III made to Friends of IHES, the partner organization of IHES in the United States. William R. Hearst III, who holds a bachelor’s degree in mathematics from Harvard, chose to name the Chair as a testimony to his friendship with the couple and his admiration for his former mathematics professor.

Gretchen and Barry Mazur have been coming to IHES since 1962, the year the Institute first moved to its current location in Bures-sur-Yvette, south of Paris. Barry recalls: “When I first came to IHES, I knew almost no mathematics. I am grateful that I learned so much and felt the inspiration of this very special Institute. Gretchen and I are truly honored to be associated with one of its Professors’ Chairs.” Initially interested in differential topology, Barry was drawn to algebraic geometry by Alexander Grothendieck, a Permanent Professor in Mathematics at IHES from 1958 to 1970, whose theory of schemes laid the foundations for modern algebraic geometry. In his paper “Modular Curves and the Eisenstein ideal”, published in “Les Publications mathématiques de l’IHES” in 1977, Barry successfully used Grothendieck’s ideas and methods to solve problems arising in number theory.

“Barry’s work truly revolutionized arithmetic geometry. Without it, Andrew Wiles’ proof of Fermat’s Last Theorem would have been impossible. It is one of the most seminal papers I have ever read,” says Emmanuel Ullmo, mathematician and Director of IHES. Alongside his work on the classification of rational points and the arithmetic of the Eisenstein ideal, Barry also made major contributions to the theory of deformations of Galois representations, Iwasawa theory, and Diophantine stability. For his achievements, Barry was awarded numerous prizes, including the Cole Prize, the National Medal of Science, and the Chern Medal.

Alexander Goncharov, first holder of the Gretchen and Barry Mazur Chair from 2019 to 2022, was deeply honored by his appointment: “I first met Barry in the 1990s at Harvard, and his universal knowledge, not only in mathematics but also in philosophy and poetry, has inspired my work ever since.” During his time at IHES, Alexander Goncharov particularly enjoyed discussing mathematics with many people at IHES, and especially Maxim Kontsevich, whom he first met as a student in Israel Gelfand’s seminar at Moscow State University. Together, they have notably worked on a non-commutative generalization of cluster varieties, objects appearing in geometry, representation theory, and mathematical physics.

Find out more about Alexander Goncharov in the interview IHES conducted with him in 2019.

Following Alexander Goncharov, IHES is delighted to announce Curtis T. McMullen as the new holder of the Gretchen and Barry Mazur Chair. Just like Gretchen and Barry, Curtis has a long history with the Institute. He first visited IHES in 1984 as a graduate student to work with Dennis Sullivan, a Permanent Professor in Mathematics at IHES from 1974 to 1998. During his visit, Curtis McMullen met Steve Smale, who ended up giving him his thesis problem on solving polynomial equations by iteration. For his doctoral work and subsequent research on Riemann surfaces, dynamics and hyperbolic 3-manifolds, he was awarded the Fields Medal in 1998. His more recent research has ranged from the geometry of numbers to the dynamics of billiards in polygons. From the mid 1980’s to the mid 1990’s, Curtis regularly visited IHES over the summer. He is enthusiastic to return to the unique scientific community at IHES and to connect with colleagues in the Paris region.

“Alexander Goncharov and Curtis T. McMullen are setting very high standards for future holders of the Gretchen and Barry Mazur Chair, and we are glad to see that in its first five years the Chair was able to attract such incredible mathematical talent to IHES. The Institute is deeply grateful to Margaret and William R. Hearst III for their support and the funding of this Chair,” concludes Emmanuel Ullmo.