A specialist in harmonic analysis, Hong Wang recently announced a solution to the three-dimensional Kakeya conjecture, a longstanding open problem at the intersection of analysis and geometry.

Originally from Guangxi, China, Hong Wang earned her undergraduate degree in mathematics from Peking University in 2011. She then moved to France, where she graduated from École Polytechnique (Cycle Ingénieur polytechnicien, X2010) and obtained a master’s degree in mathematics at Université Paris-Saclay in 2014. During her PhD at MIT, completed in 2019 under the supervision of Larry Guth, she began working on problems in Fourier analysis. Following a postdoctoral position at the Institute for Advanced Study in Princeton, she became Assistant Professor at UCLA in 2021, before joining the Courant Institute in 2023.

In 2022, Hong Wang was awarded the Maryam Mirzakhani New Frontiers Prize for “advances on the restriction conjecture, the local smoothing conjecture, and related problems.” More recently, Hong Wang and her co-author Joshua Zahl distinguished themselves by announcing the solution to the three-dimensional Kakeya conjecture, a longstanding open problem at the intersection of harmonic analysis and geometry.

Julio Parra-Martinez is a theoretical physicist working on many topics, including quantum field theory, scattering amplitudes, gravitation, effective field theories and string theory.

In recent years he has focused on importing techniques from particle physics to the realm of classical general relativity. These techniques, which were originally developed to compute the quantum probabilities of scattering events at particle colliders, have found surprising applications to gravitational-wave and black-hole physics.

Originally from Spain, Julio Parra-Martinez did his undergraduate at the University of Valencia, and his graduate studies in the UK and USA, obtaining a MASt in Applied Mathematics from the University of Cambridge in 2015, and a PhD in Physics from the University of California Los Angeles (UCLA) in 2020. After getting his PhD, he spent three years as a Sherman Fairchild Prize Postdoctoral Fellow at the California Institute of Technology (Caltech), and one year as an Assistant Professor at the University of British Columbia, in Vancouver, Canada, before he joined IHES in 2024.

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Dustin Clausen did his undergraduate studies at Harvard university, and obtained his PhD in 2013 from MIT, working on Arithmetic Duality in Algebraic K-theory, under the supervision of Jacob Lurie. He then spent five years as a postdoc in Copenhagen, followed by two years in Bonn, first as a postdoc at the University of Bonn, and then as a research group leader at the Max Planck Institute for Mathematics. He moved back to Denmark in 2020 to work as an associate professor at the University of Copenhagen.

Dustin Clausen is Principal Investigator of the Simons Collaboration on Perfection in Algebra, Geometry, and Topology.

Laure Saint-Raymond entered the École normale supérieure in 1994. During her studies, she obtained a DEA in numerical analysis at the University of Paris VI and another in plasma physics at the University of Versailles-Saint-Quentin, as well as an agrégation in mathematics. She then obtained a doctorate at the department of mathematics and applications of the ENS under the supervision of mathematician François Golse, on the kinetic theory of gases. She was recruited as a research fellow at the CNRS in 2000. She was then appointed professor at the Université Paris VI in 2002. In 2007, she was seconded to the École normale supérieure, where she headed the analysis team before becoming director of studies in the mathematics department. She was elected a member of the Académie des sciences since 2013, when she has since been a regular participant in think tanks, notably on the dissemination of knowledge. She became a junior member of the Institut Universitaire de France in 2015, after spending a sabbatical year in the United States, at the joint invitation of Harvard University and MIT. In 2016, she joined the École normale supérieure de Lyon as a university professor with the project of developing strong links between mathematics and physics.

Laure Saint-Raymond works mainly on the asymptotic analysis of systems of partial differential equations, in particular those governing gas, plasma, and fluid dynamics. In particular, she has made fundamental contributions to Hilbert’s sixth problem concerning the axiomatization of mechanics, one of the 23 problems proposed by David Hilbert at the International Mathematical Congress of 1900, which has not been solved to this day. With various collaborators, she has shown that there is a continuous transition between non-equilibrium statistical physics models and the equations of fluid mechanics, and more recently she has studied the validity of these statistical models based on Newtonian mechanics. In parallel, she works on fluid mechanics models describing ocean currents, including the influence of rotation and stratification on wave propagation and boundary layer phenomena.

This year, Slava Rychkov has uncovered a connection between Deligne categories (mathematical structures defined by Pierre Deligne in 2004), and symmetries of probabilistic loop ensembles on lattices, playing an important role in statistical physics.

His other major project was an application of renormalization group and conformal field theory to phase transitions with a random field type of disorder.

Finally, Slava Rychkov has developed a method for analytic continuation of Euclidean conformal field theories to the Lorentzian signature, which is more direct than the classic construction of Osterwalder and Schrader (1975).

Slava Rychkov is a Principal Investigatorfor the Simons Collaboration on Probabilistic Paths to Quantum Field Theory.

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Emmanuel Ullmo alternated between positions in France and abroad, including 18 months at IMPA in Brazil, two years at Princeton University in the United States and six months at Tsing-Hua University in the ­People’s Republic of China.

Professor at Université Paris-Sud in 2001, Emmanuel Ullmo became Director of the Department of Mathematics of Orsay and President of the Commission of Experts between 2007 and 2010. Member of the Scientific Council of the Centre Émile Borel from 2002 to 2006, he is also a member of the editorial board of Inventiones Mathematicae since 2006, being one of two editors-in-chief from 2008 to 2014.

Recently, Emmanuel Ullmo showed, in collaboration with Chris Daw and Alexander Gorodnik, that the space of homogeneous measures on the maximum Satake compactification of a locally symmetric space is compact. In other words, the boundary measure of a sequence of homogeneous measures is supported on a single edge component and is homogeneous. Moreover in collaboration with Gregorio Baldi, he demonstrated the finitude of the set of maximal totally geodesic subvarieties of a ball quotient unit of the complex affine space of dimension n by a non-arithmetic network.

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On the mathematical side, he has drawn on the systematic use of known algebraic structure deformations and on the introduction of new ones that turned out to be relevant in many other areas, with no obvious link.

Maxim Kontsevich is the Principal Investigator of the ERC – Synergy Grant “Recursive and Exact New Quantum Theory” (ReNew Quantum), funded by the European Union’s Horizon 2020 research and innovation program, under grant agreement #810573.

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By using new connections between these models and by developing a theory of dependent percolation, Hugo Duminil-Copin has obtained major results on these classical models and their phase transitions, thus improving our understanding of critical phenomena in statistical physics at equilibrium.

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