for his pioneering work on symplectic geometry, especially for envisioning the existence of a category — nowadays called the Fukaya category — consisting of Lagrangians on a symplectic manifold, for leading the monumental task of constructing it, and for his subsequent ground-breaking and impactful contributions to symplectic topology, mirror symmetry, and gauge theory.
The Shaw Prize in Mathematical Sciences 2025 is awarded to Kenji Fukaya, Professor at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and the Yau Mathematical Sciences Center (YMSC), Tsinghua University, PRC, for his pioneering work on symplectic geometry, especially for envisioning the existence of a category — nowadays called the Fukaya category — consisting of Lagrangians on a symplectic manifold, for leading the monumental task of constructing it, and for his subsequent ground-breaking and impactful contributions to symplectic topology, mirror symmetry, and gauge theory.
In classical mechanics, the time evolution of a physical system is described as the flow over phase space determined by a Hamiltonian function. In the 1960s, Arnold proposed conjectures in order to study the lower bound of the number of periodic solutions of the flow when the Hamiltonian is time-periodic. In modern mathematics, phase spaces are generalised to symplectic manifolds. A refined conjecture concerns a lower bound of the number of points of intersections of two Lagrangian submanifolds on a symplectic manifold.
Kenji Fukaya was born in 1959 in Yokohama, Japan and is currently a Professor of the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and the Yau Mathematical Sciences Center (YMSC) at Tsinghua University, PRC. He received his Bachelor’s degree and PhD from the University of Tokyo, Japan in 1981 and 1986 respectively. He was a Research Assistant (1983–1986) and was appointed as an Associate Professor (1987–1993) at the University of Tokyo. He then moved to Kyoto University, Japan as a Professor (1994–2013) and became a permanent member of the Simons Center for Geometry and Physics at the State University of New York at Stony Brook, USA in 2013. He has been appointed as a Professor at BIMSA and YMSC since 2024. He is a member of the Japan Academy.
