Salem Awards Shine Bright: Miguel Walsh and Wang Yilin Take Home Prestigious Honors in 2024

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Recently, it was announced on the official website of the IAS Institute for Advanced Study in Princeton that the 2024 Salem Prize will be awarded to Miguel Walsh and Wang Yilin.

Introduction to the winners and reasons for winning the awards

Miguel Walsh (1987-, Argentina)

Source: Todo Jujuy

Winner of the Salem Prize for his developments in ergodic theory, analytic number theory, and polynomial methods, his contributions include the convergence theorem for unconventional ergodic means, bounds on local Fourier uniformity of multiplicative functions, and bounds on rational points on varieties.

Yilin Wang (1991-, studied in France and Switzerland, born in Shanghai, China)

Source: Wang Yilin

Winner of the Salem Prize for establishing deep and novel connections between complex analysis, probability, and mathematical physics, particularly in Teichmuller theory and Schramm-Loewner evolutionary theory.

About Salem Prize

Source: IAS

The Salem Prize was established in 1968 and is named in honor of Raphaël Salem (1898 – 1963), a mathematician best known for his work on the Fourier stage Known for his in-depth study of the connections between numbers and number theory and his pioneering applications of probabilistic methods in these fields. He played an important role in the development of harmonic analysis in France. In particular his 1963 books “Algebraic Numbers and Fourier Analysis” and “Ensembles Parfaits et Séries Trigonométriques” (the second with Jean-Pierre Kahane), and his paper on stochastic trigonometric series with Zygmund (Acta Math. 91 (1954), 245–301) Very influential.

The prize is awarded annually to a young mathematician who is recognized for outstanding work in harmonic analysis and related topics, and the recipients, many of whom later go on to become Fields Medalists, are awarded the prize.

List of Past Winners of the Salem Awards

2024 – Miguel Walsh, Yilin Wang

Miguel Walsh (Miguel Walsh, 1987 -, Argentina)

Source: LA NACION

For his contributions to the development of ergodic theory, analytic number theory, and polynomial methods, including the convergence theorem for unconventional ergodic means, bounds on the local Fourier uniformity of multiplicative functions, and bounds on rational points on varieties.

Yilin Wang (1991 -, Swiss, born in China)

Photo credit: Chris Peus/IHES

For establishing deep and novel connections between complex analysis, probability and mathematical physics, especially in Teichmuller theory and Schramm-Loewner evolution theory.

2023 – Sarah Peluse, Julian Sahasrabudhe

Sarah Peluse (Sarah Peluse, United States)

For her contributions to additive combinatorics and related fields, including her work on quantitative density theorems for polynomial configurations of arithmetic series, which have found applications in discrete harmonic analysis and ergodic theory.

Julian Sahasrabudhe (Julian Sahasrabudhe, 1988 -, Canada)

For his contributions to harmonic analysis, probability theory, and combinatorics, including his work on the construction of flat polynomials, improving bounds on the probability of singularities in stochastic symmetric matrices, and obtaining new upper bounds on the diagonal Ramsey number.

2018 – Aleksandr Logunov

Aleksandr Logunov (Alexander Andreevich Logunov, 1989 -, Russia)

Because it introduces novel geometric combination methods in the study of elliptic eigenvalue problems. Among other results, he proved the estimation (upper bound) of the Hausdorff measure of the zero set of Laplacian eigenfunctions defined on compact smooth manifolds, as well as the estimation in harmonic analysis and differential geometry (Lower Bound), proving the conjectures of Qiu Chengtong and Nikolai Nadirashvili.

2016 – Maryna Viazovska

Maryna Viazovska (Marina Viazovska, 1984 -, Ukraine)

For his work on 8- and 24-dimensional sphere packing and modular forms.

2014 – Dmitry Chelkak

Dmitry Chelkak (Dmitry Chelkak, 1979 -, Russia)

For his research involving conformal invariance of critical points of two-dimensional lattice models, especially the Ising model of statistical mechanics, where he proved the criticality together with Fields Medalist Stanislav Smirnov Conformal invariance and universality of points. Chelkak also studied spectral theory, especially the inverse spectral problem of one-dimensional differential operators.

2013 – Lawrence Guth

Larry Guth (Larry Guth, 1977 -, United States)

For his significant contributions to geometry and combinatorics, including the strengthening of Gromov’s basic manifold contraction inequalities and, together with Nets Katz, finding the solution to Erdős’ differential distance problem. His interests include the Kakeya conjecture and systolic inequality.

2011 – Dapeng Zhan, Julien Dubédat

Dapeng Zhan (USA)

Julien Dubédat (Julian Dubédat, 1978 -, United States)

For his outstanding work on Schramm-Loewner evolution (SLE), especially the proofs of the reversibility and duality conjectures.

2010 – Nalini Anantharaman

Nalini Anantharaman (Nalini Anantharaman, 1976 -, France)

For his work on Laplace eigenfunctions and entropy.

2008 – Bo’az Klartag, Assaf Naor

Bo’az Klartag (1978-, Israel)

For his contributions to asymptotic geometric analysis.

Assaf Naor (Assaf Naor, 1975 -, Israel – United States)

For his contributions to the theory of metric space structures and their applications in computer science.

2007 – Akshay Venkatesh

(Akshay Venkatesh, 1981-, Australia, born in India)

for his work in the field of analytics. His research interests are counting, equidistributive problems in automorphic forms, and number theory, especially representation theory, locally symmetric spaces, ergodic theory, and algebraic topology.

2006 – Stefanie Petermichl, Artur Avila

Stefanie Petermichl (Stephanie Petermichl, 1971 -, Germany)

For work that had several key influences on the theory of vector-valued singular operators.

Artur Avila (Artur Avila, 1979 -, Brazil)

In 2005, Avila and Svetlana Jitomirskaya proved the “Ten Martini Conjecture” proposed by American mathematical physicist Barry Simon. Mark Kac promised ten martinis to whoever solved the problem: whether the spectrum of a particular type of operator, given certain conditions on its parameters, is a Cantor set. This question has not been solved for 25 years, and Avila and Gitomirskaya answered in the affirmative. Later in the same year, Avila and Marcelo Viana proved the Zorich-Kontsevich conjecture, that is, the non-trivial Lyapunov exponents of Teichmüller flows on Abelian differential modulus spaces on compact Riemannian surfaces are all different.

2005 – Ben Green

Ben Green (Ben Green, 1977 -, UK)

Working with Terence Tao and Tamar Ziegler, he developed so-called higher-order Fourier analysis. The theory relates the Gaussian norm to an object called a zero sequence. The theory takes its name from these zero sequences, which play a role similar to that played by features in classical Fourier analysis. Green and Tao proposed a new method for counting the number of solutions to simultaneous equations for certain sets of integers (including prime numbers) using higher-order Fourier analysis.

2003 – Elon Lindenstrauss, Kannan Soundararajan

Elon Lindenstrauss (Elon Lindenstrauss, 1970 -, Israel)

Because of his work in the field of dynamics, especially ergodic theory and its applications in number theory.

Kannan Soundararajan (1973-, American, born in India)

For its contributions to the Dirichlet L function and related features and fields

2002 – Xavier Tolsa

Xavier Tolsa (1966-, Catalonia)

His research areas include harmonic analysis (Calderón-Zygmund theory), complex analysis, geometric measure theory and potential theory. Specifically, he is known for his research on analytic capabilities and removable sets. He solved AG Vitushkin’s problem about the semi-additivity of analytic power. This allowed him to solve Paul Painlevé’s older problem on the geometric characteristics of removable sets. Tolsa successfully solved the Painlevé problem by using the so-called measure curvature concept introduced by Mark Melnikov in 1995. Tolsa’s proof involves the estimation of the Cauchy transform. He also conducted research on the so-called David-Semmes problem involving Riesz transformations and correctability.

2001 – Oded Schramm, Stanislav Smirnov

Oded Schramm (Oded Schramm, 1961-2008, American, born in Israel)

For his development of the stochastic Loewner equation and his contribution to the geometry of plane Brownian curves.

Stanislav Smirnov (Stanislav Smirnov, 1970 -, Russia)

For its study of scaling limits and conformal invariance of critical penetration in hexagonal meshes.

2000 – Terence Tao

Terence Tao (Tao Zhexuan, 1975 -, Australia – United States)

For his work on Lᴾ harmonic analysis and problems related to geometric measure theory and partial differential equations.

1999 – Fedor Nazarov

Fedor Nazarov (Fedor Nazarov, 1967 -, Russia)

For his work on harmonic analysis, especially the uncertainty principle, and for his contribution to the development of the Bellman function method.

1998 – Trevor Wooley

Trevor Wooley (Trevor Woolley, 1964 -, UK)

Because it made a major breakthrough on the Hualin issue. His areas of interest include analytic number theory, Diophantine equations and Diophantine problems, harmonic analysis, the Hardy-Littlewood circle method, and the theory and applications of exponential sums.

1996 – Michael Lacey, Christoph Thiele

Michael Lacey (Michael Lacey, 1959 -, United States)

For his research on bilinear Hilbert transforms. This transformation was then the subject of Alberto Calderón’s conjecture, which Lacey and Christoph Thiele solved in 1996.

Christoph Thiele (Christoph Thiele, 1968 -, Germany)

Known for his work (with Michael Lacey) on the bilinear Hilbert transform and for his simplified proof of Carlson’s theorem; the techniques in this proof profoundly influenced the field of time-frequency analysis.

1995 – Håkan Eliasson

Håkan Eliasson (1952 – Sweden)

Because his research involves dynamical systems, quasi-periodic motion, small denominator problems in perturbation theory, KAM theory and multi-scale analysis in perturbation theory, Hamiltonian partial differential equations, and localization and diffusion in quasi-periodic Schrödinger operators .

1994 – Kari Astala

Kari Astala (Kari Astala, 1953 -, Finland)

For its application of dynamical systems theory to solve the conjectures of Frederick Gehring (1925-2012) and Edgar Reich (1927-2009) in quasi-conformal mapping theory

1993 – Sergei Treil

Sergei Treil (Sergei Treil, Russia)

Because of his important research in the intersection of operator theory, complex analysis and harmonic analysis. Most of his research is on problems related to applied mathematics, such as control theory, stationary stochastic processes, signal processing, and wavelets. His research interests include Hankel operators, Toeplitz operators, operator function models, operator spectral decomposition, spectral theory of matrices and operator-valued functions, the Corona problem, and the interaction between operator theory and complex geometry.

1992 – Mitsuo Shishikura

Mitsuo Shishikura (Mitsuhiro Shishikura, 1960 -, Japan)

Internationally recognized for his two earliest contributions, both of which solved long-standing open problems: in his master’s thesis he showed that rational functions of degree d have at most 2d-2 non-exclusive periods Ring, which proved Fatou’s conjecture in 1920; he proved that the boundary of the Mandelbrot set has Hausdorff two dimensions, confirming the conjecture proposed by Mandelbrot and Milnor.

1991 – Curtis Tracy McMullen

Curtis Tracy McMullen (Curtis Tracy McMullen, 1958 -, United States)

For his work on complex dynamics, hyperbolic geometry and Teichmüller theory.

1990 – Sergei Vladimirovich Konyagin

Sergei Vladimirovich Konyagin (1957-, Russia)

For its application of harmonic analysis to number theory settings.

1988 – Alexander Volberg, Jean-Christophe Yoccoz

Alexander Volberg (Alexander Volberg, 1956 -, Russia)

For his contributions to harmonic analysis and its relationship to geometric measure theory.

Jean-Christophe Yoccoz (Jean-Christophe Yoccoz, 1957-2016, France)

Because of his commitment to dynamical systems theory. His contributions include advances in KAM theory and the introduction of the Yoccoz puzzle method, a combinatorial technique that has proven useful in the study of Julia sets.

1987 – Guy David, Jean-Lin Journé

Guy David (Guy David, 1957 -, France)

Jean-Lin Journé (Jean-Lin Journé, 1957-2016, France)

Together they prove the T(1) theorem.

1986 – Nikolai Georgievich Makarov

Nikolai Georgievich Makarov (Nikolai Georgievich Makarov, 1955, Russia)

Its solution involves the use of stochastic methods to conformally map a disk to the boundary behavior of a domain with approximately equivalent curvilinear boundaries.

1985 – Thomas H. Wolff

Thomas H. Wolff (Thomas Wolff, 1954-2000, United States)

For his contribution to analysis, especially the Kakeya conjecture.

1984 – Carlos Kenig (Carlos Kenig, 1953 -, United States)

Carlos Kenig

For his extensive work on elliptic and dispersive partial differential equations.

1983 – Jean Bourgain

Jean Bourgain (Jean Bourgain, 1954-2018, Belgium)

His research work included many areas of mathematical analysis, such as Banach space geometry, harmonic analysis, analytic number theory, combinatorics, ergodic theory, partial differential equations and spectral theory, and later group theory. He proved the uniqueness of the solution to the initial value problem of the Korteweg-De Vries equation. He formulated what became known as the Burgan slice problem in high-dimensional convex geometry.

1982 – Alexei Borisovich Aleksandrov

(No photos yet)

Alexei Borisovich Aleksandrov (Alexei Borisovich Alexandrov, 1954 -, Russia)

His research involves topics such as function theory in the unit sphere, Hardy spaces, shift operators and Hadamard gap series.

1981 – Peter Jones

Peter Jones (Peter Jones, 1952 -, United States)

For his work on harmonic analysis and fractal geometry.

1980 – Stylianos Pichorides

Stylianos Pichorides (Stylianos Pichorides, 1940-1992, Greece)

For his research on Littlewood’s average exponent and lower bound conjecture.

1979 – Gilles Pisier

Gilles Pisier (Gills Pisier, 1950 -, France)

For his contributions to functional analysis, probability theory, harmonic analysis, and operator theory.

1978 – Björn E. Dahlberg

Björn E. Dahlberg (1949-1998, Sweden)

For his contributions to harmonic analysis and partial differential equations.

1977 – Sergei Viktorovich Bochkarev

Source: mi.ras.ru

SV Bockarev (Sergey Viktorovich Bochkarev, 1941-2021, Russia)

For his research on harmonic analysis, BMO spaces, Hardy spaces, functional analysis, the construction of orthogonal bases in various function spaces, and exponential sums.

1976 – Michaël Robert Herman

Michaël Robert Herman (Michael Robert Herman, 1942-2000, American, French)

for his research on dynamical systems. http://assets.cambridge.org/052186/0687/excerpt/0521860687_excerpt.pdf

1975 – William Beckner

William Beckner (William Beckner, 1941 -, United States)

For his work on harmonic analysis, especially geometric inequalities.

1974 – Hugh Montgomery

Hugh Montgomery (Hugh Lowell Montgomery, 1944 -, United States)

For his pairing-related conjectures, the development of the grand sieve method, and his co-authorship (with Ivan M. Niven and Herbert Zuckerman) of one of the standard introductory number theory texts, Introduction to Number Theory.

1973 – Evgenii Mikhailovich Nikishin

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Evgenii Mikhailovich Nikishin (Yevgeni Nikishin, 1945-1986, Russia)

Because he is committed to the study of approximation theory, especially Padé approximation theory. The Nikishin function system is named after him. Also named after him is the Nikishin-Stein factorization theorem, which is Nikishin’s generalization of Stein’s factorization theorem in 1970. Nikishin also studied rational approximations in number theory and wrote a monograph on such approximations in a unified approach that also dealt with rational approximations in function spaces.

1972 – Thomas William Körner

Thomas William Körner (Thomas William Körner, 1946 -, United Kingdom)

For his work on Fourier analysis and so on. He has also written popular mathematics books for undergraduates and middle school students.

1971 – Charles Fefferman

Charles Fefferman (Charles Fefferman, 1949 -, United States)

For his work on partial differential equations, Fourier analysis (especially convergence, multipliers, divergence, singular integrals and Hardy spaces).

1970 – Yves Meyer

Yves Meyer (Yves Meyer, 1939 -, France)

For his fundamental contributions to number theory, operator theory and harmonic analysis, and his key role in the development of wavelets and multi-resolution analysis (MRA)

1969 – Richard Allen Hunt

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Richard Allen Hunt (Richard Allen Hunt, 1937-2009, United States)

Because of its research: the Fourier expansion of the function in Lᴾ, p>1 converges almost everywhere. The case p=2 was proposed by Lennart Carleson, so the general result is called the Carleson-Hunt theorem.

1968 – Nicolas Theodore Varopoulos

(No photos yet)

Nicolas Theodore Varopoulos (Nicolas Theodore Varopoulos, 1940 -, Greece)

For his work on harmonic analysis, especially Lie group analysis.

References

https://www.ias.edu/math/2024-salem-prize-winners

https://en.wikipedia.org/wiki/Salem_Prize

https://www.ias.edu/math/activities/salem-prize

https://www.ias.edu/paths-to-math

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