Yakov Eliashberg receives 2024 Frontiers of Knowledge Award

Yakov Eliashberg, the Herald L. and Caroline L. Ritch Professor in Humanities and Sciences and professor of mathematics in H&S, and Claire Voisin of the National Center for Scientific Research, France, shared a 2024 Frontiers of Knowledge Award in Basic Sciences from the BBVA Foundation for research that advanced the field of mathematics by bridging the fields of algebraic and symplectic geometry.

The BBVA Foundation Frontiers of Knowledge Awards recognize fundamental contributions in eight domains—basic sciences (physics, chemistry, and mathematics); biology and biomedicine; information and communication technologies; ecology and conservation biology; climate change; economics, finance, and management; humanities and social sciences; and music and opera.

“I am honored to have my work recognized by this prestigious award and especially happy to share the prize with an outstanding algebraic geometer Claire Voisin,” Eliashberg said.

Eliashberg’s research focuses on symplectic geometry and the related field of symplectic topology. The origins of symplectic geometry trace back to the work of 19th-century mathematicians William Rowan Hamilton and Carl Gustav Jacob Jacobi. Symplectic geometry has found applications beyond classical mechanics in quantum mechanics, other areas of mathematics, physics, and engineering. Eliashberg’s contributions helped establish the younger area of symplectic topology, which has found new connections and applications to other areas of mathematics and physics.

Eliashberg’s research “has fundamentally transformed several areas of geometry, created some new ones, and revealed unexpected connections between previously unrelated fields,” said his nominator for the award, Kai Cieliebak, professor of analysis and geometry at the University of Augsburg, Germany, in the award announcement.

“At the beginning of the 20th century, symplectic topology was a dream of Henri Poincaré for answering qualitative problems of mechanics,” Eliashberg said. “In the 1980s, it was born as a mathematical subject, thanks to the work of several great mathematicians, primarily Mikhail Gromov, as well as Andreas Floer, Helmut Hofer, Dusa McDuff, Alan Weinstein, Eduard Zehnder, and others. I was lucky to be present at the birth of this area and to be able to contribute to its development.”

Nigel Hitchin, the Savilian Professor of Geometry, Emeritus, at the University of Oxford and a BBVA award committee member remarked on Eliashberg’s significant contributions to the field of mathematics in the award citation stating, “for researchers in our discipline, there’s no greater stimulus than when you break down the barriers between two areas. By doing that you can adopt a new language, possibly a new framework, a new way of looking at things from the other side, which enables you to make further progress.”

“I believe that both in mathematics and science in general, the most wonderful results come from discovering the connections between seemingly different things,” said Eliashberg in the award announcement. “I am excited by different areas of mathematics working together and the fruits that may come from discovering unsuspected links.”

Since the awards were established in 2008 by the BBVA Foundation, 14 Stanford faculty have received BBVA Foundation Frontiers of Knowledge Awards in various categories.