Search Clay Mathematics Institute

  • About
    About
    • About
    • History
    • Principal Activities
    • Who’s Who
    • CMI Logo
    • Policies
  • Programs & Awards
    Programs & Awards
    • Programs & Awards
    • Funded programs
    • Fellowship Nominations
    • Clay Research Award
    • Dissemination Award
  • People
  • The Millennium Prize Problems
    The Millennium Prize Problems
    • The Millennium Prize Problems
    • Birch and Swinnerton-Dyer Conjecture
    • Hodge Conjecture
    • Navier-Stokes Equation
    • P vs NP
    • Poincaré Conjecture
    • Riemann Hypothesis
    • Yang-Mills & the Mass Gap
    • Rules for the Millennium Prize Problems
  • Online resources
    Online resources
    • Online resources
    • Books
    • Video Library
    • Lecture notes
    • Collections
      Collections
      • Collections
      • Euclid’s Elements
      • Ada Lovelace’s Mathematical Papers
      • Collected Works of James G. Arthur
      • Klein Protokolle
      • Notes of the talks at the I.M.Gelfand Seminar
      • Quillen Notebooks
      • Riemann’s 1859 Manuscript
  • Events
  • News

Home — News — 2024 Clay Research Award

2024 Clay Research Award

Date: 01 May 2024

Image of the Clay Research Award
Newton and Thorne

James Newton and Jack Thorne

A Clay Research Award is made to James Newton (Oxford) 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.

Paul Nelson

Paul Nelson

A Clay Research Award is made to Paul Nelson (Aarhus) 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 signficant advance in a field initiated one hundred years ago by Hermann Weyl in the context of the Riemann Zeta function.  Nelson analyzes 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.

Share

More news

See all news
17 March 2025

STEM for Britain 2025

Congratulations to Edwina Yeo (University College London), winner of The Parliamentary & Scientific Committee’s STEM for Britain Gold Medal, sponsored by CMI, for her poster Preventing bacterial surface contamination via mathematical modelling.

Read more
12 February 2025

Babbage Archive

Oxford’s History of Science Museum holds important material associated with Charles Babbage, including components of Babbage’s first (unfinished) mechanical computing machine and an archive of his personal notes about his machines. With support from CMI, the Museum undertook a project to conserve and digitise this precious archive of Babbage material. Image courtesy of the History […]

Read more
2025 Clay Research Fellows
16 January 2025

2025 Clay Research Fellows

The Clay Mathematics Institute is pleased to announce that Ryan Chen, Alex Cohen and Anna Skorobogatova have been awarded Clay Research Fellowships. Ryan Chen will receive his PhD from the Massachusetts Institute of Technology in 2025, where he works under the guidance of Wei Zhang. Ryan has been appointed as a Clay Research Fellow for […]

Read more
22 April 2024

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 […]

Read more
See all news
  • Privacy Policy
  • Contact CMI

© 2025 Clay Mathematics Institute

Site by One