Yu Deng

For his work in partial differential equations, including the rigorous derivation of the Boltzmann equation from hard-sphere dynamics for rarefied gases, the derivation of wave kinetic equations from nonlinear dispersive systems, and probabilistic approaches to nonlinear Schrodinger dynamics. 

Combining techniques from partial differential equations, probability, and mathematical physics, Yu Deng has made fundamental contributions to the rigorous analysis of complex dynamical systems, clarifying how macroscopic and statistical behavior emerge from microscopic dynamics. Together with Zaher Hani and Xiao Ma, Deng achieved landmark results on the derivation of the Boltzmann equation from deterministic hard-sphere dynamics in the low-density regime. His work provides a rigorous derivation of Boltzmann’s equation for rarefied gases, valid for as long as the corresponding Boltzmann solution exists, overcoming longstanding obstacles in connecting Newtonian particle systems with kinetic theory and addressing a central problem in nonequilibrium statistical mechanics. In joint work with Hani, Deng made major advances in the derivation of wave kinetic equations from nonlinear dispersive systems. These results explain how statistical behavior and energy transfer arise from deterministic nonlinear dynamics, contributing significantly to the mathematical foundations of wave turbulence theory. Beyond kinetic limits, together with Andrea Nahmod and Haitian Yue, Deng developed innovative probabilistic approaches to nonlinear Schro dinger equations (such as random averaging operator and random tensor theories), yielding new insights into long-time behavior, propagation of randomness, and stability for nonlinear dispersive partial differential equations. His work has substantially expanded the scope of rigorous analysis in nonlinear dynamics and has had a deep impact on the study of dispersive equations and mathematical physics.

John Pardon

For his achievements in symplectic geometry including new approaches to virtual fundamental cycles, Fukaya categories of certain manifolds and counting holomorphic curves, and for his contributions to other areas of geometry and topology, including group actions on 3-manifolds and knot theory.

John Pardon is a mathematician of extraordinary depth and originality, who has repeatedly had a significant impact on the fields of topology and symplectic geometry. He has both contributed to fundamental structure and solved problems that had stymied the community for decades. In topology Pardon answered an old question of Gromov about the distortion of torus knots. He went on to give a big progress on the 70 years old Hilbert-Smith conjecture, which states that a locally compact topological group that acts faithfully on a connected 𝓃 -manifold must be a Lie group, by proving the conjecture for 𝓃 = 3. In symplectic geometry Pardon’s first important paper transported techniques from algebraic topology to give an alternate construction of virtual fundamental cycles for moduli spaces of pseudo-holomorphic curves. He applied his machinery to several problems in symplectic geometry, for example, a proof of Arnold conjecture, originally due to Fukaya-Ono, Liu-Tian and Ruan, a definition of contact homology proposed by Eliashberg-Givental-Hofer, and so on. Another of Pardon’s striking achievements is contained in a series of papers with Ganatra and Shende on computations and structural results concerning wrapped Fukaya categories of certain non-compact symplectic manifolds, conjectured by Kontsevich and Nadler. Most recently, Pardon made a major breakthrough in enumerative geometry, namely in the problem of comparing different methods that have been proposed to count curves in certain complex 3-folds. Maulik, Nekrasov, Okounkov and Pandharipande had conjectured a deep and surprising connection between the generating functions for Gromov-Witten invariants and Donaldson-Thomas invariants. Pardon proposed a highly innovative approach to this problem when the anti-canonical bundle is nef.

Jacob Tsimerman

For his contribution in the recasting of o-minimality as a fundamental method of arithmetic and complex algebraic geometry, and his role in the proof of many central conjectures including Griffiths' conjecture on the algebraicity of images of the period maps, and the André-Oort conjecture for Siegel modular varieties.

Extending the method of o-minimality and combining it with ideas from a broad range of areas of mathematics, Jacob Tsimerman, with his collaborators, has solved several major problems in arithmetic and complex algebraic geometry. The development of o-minimal theory in the holomorphic setting was initiated by Peterzil and Starchenko, who established an affine version of Chow's algebraicity theorem. With Bakker and Brunebarbe, Tsimerman extended this theory to a full-fledged GAGA theorem over possibly non reduced complex spaces. Combining it with the earlier work of Bakker, Klingler and Tsimerman that placed period maps in the o-minimal domain, they proved Griffiths' conjecture on the algebraicity of images of the period maps, a long-standing problem in Hodge theory. The André-Oort conjecture was a central problem in the Diophantine geometry of Shimura varieties, predicting subvarieties containing many special points are special subvarieties. Following a proof assuming the generalized Riemann hypothesis by Edixhoven, Klingler, Ullmo and Yafaev, Pila and Zannier formulated a strategy for an unconditional proof, using o-minimality via the Pila-Wilkie estimates. Tsimerman played a key role in the development, contributing to the two parts of the Pila-Zannier strategy: Galois lower bounds (using the average Colmez conjecture as a key ingredient) and functional transcendence (Ax-Lindemann, obtained jointly with Pila).  As a consequence, Tsimerman completed the proof for Siegel modular varieties. A stronger functional transcendence statement, Ax-Schanuel, is of interest on its own and in connection with the Zilber-Pink conjecture. Mok, Pila and Tsimerman have used o-minimality combined with number-theoretic and geometric techniques to prove the Ax-Schanuel conjecture for Shimura varieties. With Bakker, and using general Ax-Schanuel results obtained independently by Blazques-Sanz, Casales, Freitag and Nagloo, by Chiu and by Gao-Klingler, Tsimerman formulated and proved a functional version of the André-Grothendieck conjecture on transcendence of periods.

Hong Wang

For her work in harmonic analysis and geometric measure theory, including applications of multiscale and decoupling techniques to the local smoothing conjecture for the planar wave equation, and major advances in Fourier restriction, Falconer distance sets, Furstenberg sets in the plane, and the Kakeya problem in three dimensions.

Extending and refining modern techniques in harmonic analysis and geometric measure theory, Hong Wang has achieved a series of major breakthroughs on some of the most central problems in analysis, combining multiscale methods with deep geometric and combinatorial insights.   Wang has played a decisive role in advancing the theory of local smoothing for wave equations. Together with Larry Guth and Ruixiang Zhang, she introduced powerful decoupling and multiscale arguments to resolve the local smoothing conjecture for the planar wave equation. Her work has also led to fundamental progress in Fourier restriction theory and in geometric problems related to distance sets. In particular, with Guth, Alex Iosevich, and Yumeng Ou, she obtained major results on the Falconer distance set problem, clarifying the relationship between Hausdorff dimension and the structure of distance distributions. In addition, with Kevin Ren, she made breakthrough contributions to the theory of Furstenberg sets in the plane, significantly deepening the understanding of directional phenomena in fractal geometry. In higher dimensions, Wang has achieved major advances on the Kakeya problem in three dimensions. In joint work with Joshua Zahl, she developed new bounds and structural techniques for collections of thin tubes, opening new directions and reshaping current approaches to this central problem. More broadly, her work has introduced methods that are now central to contemporary harmonic analysis and continue to influence a wide range of problems in analysis, geometry, and beyond.

（来源：国际数学联盟）