Boris A. Khesin

Boris A. Khesin
Name	Boris A. Khesin
Birth date	1956
Birth place	Leningrad, Russian SFSR
Nationality	Russian-American
Fields	Mathematics
Institutions	University of Toronto; Fields Institute; University of California, Berkeley; Massachusetts Institute of Technology; Stanford University; University of Chicago
Alma mater	Leningrad State University; Steklov Institute of Mathematics
Doctoral advisor	Vladimir Arnold
Known for	Infinite-dimensional geometry, diffeomorphism groups, integrable systems, Euler equation on groups

Boris A. Khesin is a mathematician known for work in infinite-dimensional geometry, group-theoretic approaches to fluid dynamics, and integrable systems. His research connects analytic methods from the Steklov Institute tradition with geometric viewpoints developed in seminars associated with the Moscow State University, Vladimir Arnold, and western institutions such as University of California, Berkeley and Massachusetts Institute of Technology.

Early life and education

Born in Leningrad, he studied mathematics at Leningrad State University and completed graduate work at the Steklov Institute of Mathematics under the supervision of Vladimir Arnold. His formative years included participation in seminars linked to Moscow State University, interactions with mathematicians from the International Mathematical Union circuits, and engagement with schools influenced by Andrey Kolmogorov, Israel Gelfand, and Sergei Novikov.

Research and contributions

Khesin's contributions span the geometry of infinite-dimensional groups such as diffeomorphism groups and the application of those structures to the Euler equation and ideal fluid dynamics. He developed connections between the Euler–Arnold framework associated with Vladimir Arnold and integrable systems studied by Mikhail Krichever, Igor Krichever, and Boris Dubrovin. His work on geodesic flows on groups of diffeomorphisms interfaces with research by Shlomo Sternberg, Stephen Smale, and Daniel E. Feldman while also drawing on concepts from Élie Cartan and Sophus Lie.

He investigated bi-Hamiltonian structures and Poisson geometry in contexts related to the KdV equation, Camassa–Holm equation, and related shallow water models, connecting to developments by Peter Lax, Martin Kruskal, and Constantin Charlier (Constantin); his analyses often employ techniques from the theory of coadjoint orbits of groups such as Diff(S^1), studied alongside work by Kirillov, Segal, and Pressley–Segal. Khesin contributed to classification problems for integrable PDEs and to the understanding of singularity formation in fluid models, situating his results within frameworks used by Yakov Sinai, Andrey Shabat, and Robert MacKay.

His collaborations and expositions linked topics from symplectic geometry as developed by Alan Weinstein and Jean-Marie Souriau to modern studies of topological hydrodynamics influenced by William Thurston and Boris A. Khesin's peers in low-dimensional topology including Dennis Sullivan and John Milnor. He has explored relations between foliation theory from Alain Connes-inspired noncommutative geometry and the topology of hydrodynamical invariants, referencing work of Vladimir Igorevich Arnold, Mikhael Gromov, and Michael Atiyah.

Academic positions and affiliations

Khesin has held positions at institutions including the University of Toronto and the Fields Institute, with visiting appointments at University of California, Berkeley, Massachusetts Institute of Technology, Stanford University, and the University of Chicago. He has been involved in programs organized by the International Centre for Theoretical Physics, the Simons Foundation, and research networks funded by bodies such as the National Science Foundation and the Natural Sciences and Engineering Research Council of Canada. He has served on editorial boards of journals associated with the American Mathematical Society and collaborated with research groups at the Steklov Institute of Mathematics and the Institute for Advanced Study.

Awards and honors

He has received recognition in the form of fellowships and invitations to speak at conferences such as the International Congress of Mathematicians, the European Congress of Mathematics, and thematic meetings organized by the American Mathematical Society and the Royal Society. His honors include lectureships and awards supported by organizations like the Fields Institute and the Clay Mathematics Institute, alongside invited addresses at institutes such as the Max Planck Institute for Mathematics and the Institut des Hautes Études Scientifiques.

Selected publications

- Khesin, B.; work on diffeomorphism groups and Euler equations in leading journals linked to the American Mathematical Society and Springer. - Monographs and surveys on infinite-dimensional geometry and hydrodynamics presented at venues including the Institute for Advanced Study and IHES. - Collaborative papers with researchers connected to Steklov Institute of Mathematics, University of Toronto, and UC Berkeley on integrable systems such as the Camassa–Holm equation and KdV equation.

Teaching and mentorship

Khesin has supervised graduate students and postdoctoral researchers in programs at University of Toronto and visiting programs at Massachusetts Institute of Technology and Stanford University. His pedagogical contributions include advanced courses on geometric mechanics reflecting traditions from Vladimir Arnold and seminars modeled on the Steklov Institute of Mathematics and Moscow State University research schools.

Category:Russian mathematicians Category:Geometric mechanics