Breakthrough New Horizons in Mathematics Prize

Ewain Gwynne won the Breakthrough New Horizons in Mathematics For contributions to conformal probability, in particular to the understanding of the LQG metric.

John Pardon won the Breakthrough New Horizons in Mathematics For contributions to symplectic topology and other areas of geometry and topology.

Sam Raskin won the Breakthrough New Horizons in Mathematics For contributions to the geometric Langlands program, including the theory of the Whittaker model and the proof of the geometric Langlands conjecture in characteristic 0.

Roland Bauerschmidt won the Breakthrough New Horizons in Mathematics For outstanding contributions to probability theory and the development of renormalisation group techniques.

Michael Groechenig won the Breakthrough New Horizons in Mathematics For contributions to the theory of rigid local systems and applications of p-adic integration to mirror symmetry and the fundamental lemma.

Angkana Rüland won the Breakthrough New Horizons in Mathematics For contributions to applied analysis, in particular the analysis of microstructure in solid-solid phase transitions and the theory of inverse problems.

Ana Caraiani won the Breakthrough New Horizons in Mathematics For diverse transformative contributions to the Langlands program, and in particular for work with Peter Scholze on the Hodge-Tate period map for Shimura varieties and its applications.

Ronen Eldan won the Breakthrough New Horizons in Mathematics For the creation of the stochastic localization method, that has led to significant progress in several open problems in high-dimensional geometry and probability, including Jean Bourgain's slicing problem and the KLS conjecture.

James Maynard won the Breakthrough New Horizons in Mathematics For multiple contributions to analytic number theory, and in particular to the distribution of prime numbers.

Aaron Brown won the Breakthrough New Horizons in Mathematics For contributions to the proof of Zimmer’s conjecture.

Sebastian Hurtado Salazar won the Breakthrough New Horizons in Mathematics For contributions to the proof of Zimmer’s conjecture.

Jack Thorne won the Breakthrough New Horizons in Mathematics For transformative contributions to diverse areas of algebraic number theory, and in particular for the proof, in collaboration with James Newton, of the automorphy of all symmetric powers of a holomorphic modular newform.

Jacob Tsimerman won the Breakthrough New Horizons in Mathematics For outstanding work in analytic number theory and arithmetic geometry, including breakthroughs on the André-Oort and Griffiths conjectures.

Bhargav Bhatt won the Breakthrough New Horizons in Mathematics For outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories.

Aleksandr Logunov won the Breakthrough New Horizons in Mathematics For novel techniques to study solutions to elliptic equations, and their application to long-standing problems in nodal geometry.

Song Sun won the Breakthrough New Horizons in Mathematics For many groundbreaking contributions to complex differential geometry, including existence results for Kahler-Einstein metrics and connections with moduli questions and singularities.

Emmy Murphy won the Breakthrough New Horizons in Mathematics For contributions to symplectic and contact geometry, in particular the introduction of notions of loose Legendrian submanifolds and, with Matthew Strom Borman and Yakov Eliashberg, overtwisted contact structures in higher dimensions.

Tim Austin won the Breakthrough New Horizons in Mathematics For multiple contributions to ergodic theory, most notably the solution of the weak Pinsker conjecture.

Xinwen Zhu won the Breakthrough New Horizons in Mathematics For work in arithmetic algebraic geometry including applications to the theory of Shimura varieties and the Riemann-Hilbert problem for p-adic varieties.

Karim Adiprasito won the Breakthrough New Horizons in Mathematics For the development, with Eric Katz, of combinatorial Hodge theory leading to the resolution of the log-concavity conjecture of Rota.

June Huh won the Breakthrough New Horizons in Mathematics For the development, with Eric Katz, of combinatorial Hodge theory leading to the resolution of the log-concavity conjecture of Rota.

Kaisa Matomäki won the Breakthrough New Horizons in Mathematics For fundamental breakthroughs in the understanding of local correlations of values of multiplicative functions.

Maksym Radziwill won the Breakthrough New Horizons in Mathematics For fundamental breakthroughs in the understanding of local correlations of values of multiplicative functions.

Chenyang Xu won the Breakthrough New Horizons in Mathematics For major advances in the minimal model program and applications to the moduli of algebraic varieties.

Zhiwei Yun won the Breakthrough New Horizons in Mathematics For deep work on the global Gan-Gross-Prasad conjecture and the discovery of geometric interpretations for the higher derivatives of L-functions in the function field case.

Wei Zhang won the Breakthrough New Horizons in Mathematics For deep work on the global Gan-Gross-Prasad conjecture and the discovery of geometric interpretations for the higher derivatives of L-functions in the function field case.

Maryna Viazovska won the Breakthrough New Horizons in Mathematics For remarkable application of the theory of modular forms to the sphere packing problem in special dimensions.

Aaron Naber won the Breakthrough New Horizons in Mathematics For work in geometric analysis and Riemannian geometry, introducing powerful new techniques to solve outstanding problems, particularly for manifolds with Ricci curvature bounds.

Geordie Williamson won the Breakthrough New Horizons in Mathematics For pioneering work in geometric representation theory, including the development of Hodge theory for Soergel bimodules and the proof of the Kazhdan-Lusztig conjectures for general Coxeter groups.

Benjamin Elias won the Breakthrough New Horizons in Mathematics For pioneering work in geometric representation theory, including the development of Hodge theory for Soergel bimodules and the proof of the Kazhdan-Lusztig conjectures for general Coxeter groups.

Hugo Duminil-Copin won the Breakthrough New Horizons in Mathematics For brilliant solutions to multiple landmark problems in probability, particularly regarding critical phenomena for Ising-type models.

Mohammed Abouzaid won the Breakthrough New Horizons in Mathematics For distinguishing cotangent bundles of exotic spheres, constructing the wrapped Fukaya category with Paul Seidel, and other decisive contributions to symplectic topology and mirror symmetry.

Larry Guth won the Breakthrough New Horizons in Mathematics For ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry.

André Arroja Neves won the Breakthrough New Horizons in Mathematics For outstanding contributions to several areas of differential geometry, including work on scalar curvature, geometric flows, and his solution with Fernando Codá Marques of the 50-year-old Willmore Conjecture.