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James Newton

A Clay Research Award is made to James Newton and Jack Thorne (Cambridge) in recognition of their remarkable proof of the existence of the symmetric power functorial lift for Hilbert modular forms.

The conjecture that the symmetric powers of automorphic representations associated to classical and Hilbert modular forms should themselves be automorphic is one of the fundamental conjectures of the programme introduced by Langlands in the late 1960’s, indeed it was cited by Langlands as a prototype test case for his conjectures. Building on earlier work of Clozel and Thorne, Newton and Thorne have written a series of ingenious papers proving this result using a very detailed application of modularity lifting results to the associated Galois representations. The proof marks a milestone in work on the Langlands programme.

Photo: David Tett Photography

Paul Nelson

A Clay Research Award is made to Paul Nelson in recognition of his groundbreaking contributions to the analytic theory of automorphic forms. His work has resulted in the first convexity-breaking bounds for a large class of L-functions on the critical line (including all the standard ones of GL(n)). This marks a significant advance in a field initiated one hundred years ago by Hermann Weyl in the context of the Riemann Zeta function. Nelson analyses L-values via certain associated automorphic periods. His powerful approach involves many ingredients, including a refinement of the orbit method that he developed in earlier work with Venkatesh, and an analysis of the geometric side of an appropriate Relative Trace Formula, which facilitates the use of Amplification.

Jack Thorne

A Clay Research Award is made to Jack Thorne and James Newton (Oxford) in recognition of their remarkable proof of the existence of the symmetric power functorial lift for Hilbert modular forms.

The conjecture that the symmetric powers of automorphic representations associated to classical and Hilbert modular forms should themselves be automorphic is one of the fundamental conjectures of the programme introduced by Langlands in the late 1960’s, indeed it was cited by Langlands as a prototype test case for his conjectures. Building on earlier work of Clozel and Thorne, Newton and Thorne have written a series of ingenious papers proving this result using a very detailed application of modularity lifting results to the associated Galois representations. The proof marks a milestone in work on the Langlands programme.

STEM for Britain

Congratulations to Daniel Graham (Surrey) who won the Gold Medal for Mathematical Sciences at the 2024 STEM for Britain poster completion for his poster Passwordless Authentication in a Quantum Future. Daniel was among 20 researchers in mathematics presenting their work to politicians and a panel of expert judges in the House of Commons on March 4, 2024.

Photo courtesy of John Deehan Photography and the Parliamentary & Scientific Committee

Abelian Varieties 2

Barry Mazur’s Clay Lecture presented at the Arizona Winter School, March 5, 2024

Details

Speaker: Barry Mazur (Harvard)

Abelian Varieties 1

Barry Mazur’s Clay Lecture presented at the Arizona Winter School, March 2, 2024

Details

Speaker: Barry Mazur (Harvard)

Aravind Asok

Professor Aravind Asok has been appointed as a Clay Senior School to participate in the IAS/PCMI program Motivic Homotopy Theory.

Fabien Morel

Professor Fabien Morel has been appointed as a Clay Senior School to participate in the IAS/PCMI program Motivic Homotopy Theory.

2024 Clay Research Fellows

The Clay Mathematics Institute is pleased to announce that Ishan Levy and Mehtaab Sawhney have been awarded Clay Research Fellowships.

Ishan Levy will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Michael Hopkins. Ishan has been appointed as a Clay Research Fellow for five years beginning 1 July 2024.

Mehtaab Sawhney will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Yufei Zhao.  Mehtaab has been appointed as a Clay Research Fellow for five years beginning 1 July 2024.

Mehtaab Sawhney

Mehtaab Sawhney will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Yufei Zhao.

While still a graduate student, Sawhney has achieved a stunning number of breakthroughs on fundamental problems across extremal combinatorics, probability theory, and theoretical computer science. He is a highly collaborative researcher whose partnership with Ashwin Sah has been particularly fruitful. His remarkable body of work has already transformed swathes of combinatorics. For example, working with Kwan, Sah and Simkin, he proved a 1973 conjecture of Erdős on the existence of high-girth Steiner triple systems; with Keevash and Sah he established the existence of subspace designs; with Jain and Sah he established sharp estimates for the singularity probability in a wide class of discrete random matrices; with Sah and Sahasrabudhe he showed the existence of the spectral distribution of sparse directed Erdős–Rényi graphs; and with Kwan, Sah and Sauermann, he developed highly novel tools in anti-concentration in order to prove the Erdős- McKay conjecture concerning edge statistics in Ramsey graphs.

Mehtaab was appointed as a Clay Research Fellow for a term of five years from 1 July 2024.

Photo: Mehtaab Sawhney

Ishan Levy

Ishan Levy will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Michael Hopkins.

Levy is known for his deep and ingenious contributions to homotopy theory. His new techniques in algebraic K-theory have led to solutions of many old problems. In joint work with Burklund he established the rational convergence of the “Waldhausen tower” interpolating between the K-theory of the integers and one of the most important moduli spaces in the study of high dimensional manifolds, A(pt). He is most renowned for his work Ravenel’s “Telescope Conjecture.”

In the late 1970s Ravenel made a series of deep conjectures outlining a rich conceptual vision of stable homotopy. By the mid 1980s all but the Telescope Conjecture had been proved. For over 40 years this remained the most important problem in this part of homotopy theory. Levy’s methods in K-theory led him, Burklund, Hahn and Schlank, to the construction of counterexamples, and, in joint work with Burklund, Carmeli, Hahn, Schlank and Yanovski, to an estimate of the growth rate of the stable homotopy groups of spheres that was completely untouchable by previous methods.

Ishan was appointed as a Clay Research Fellow for a term of five years from 1 July 2024.

Photo: Archives of the Mathematisches Forschungsinstitut Oberwolfach

André Neves

Professor André Neves has been appointed as a Clay Senior Scholar to participate in New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetry at the Simons Laufer Mathematical Research Institute.