Yesterday the BBVA Foundation announced the winners of the 16th edition of the Frontiers of Knowledge awards in the basic sciences category. Researchers Yakov Eliashberg, from Stanford University in the United States, and Claire Voisin, from the National Center for Scientific Research CNRS in France, have been the winners of this award for promoting mathematical thinking and drawing parallels between algebraic and symplectic geometry. two key areas of this discipline.
Both winners have made “outstanding contributions” to the mathematical world, according to the jury itself, and have built bridges between the two disciplines.
Voisin has worked with algebraic geometry, a classic field of mathematics that begins with the resolution of simple polynomial equations from a geometric point of view. “Mathematics is a source of wisdom,” said the winner. When she studied at university she discovered her fascination with algebra, but it was not until the beginning of her career as a researcher that she began to think about a possible relationship between algebraic and symplectic geometry, because both were relevant in physics. She has now demonstrated, together with Eliashberg, that she has contributed to laying the foundations of symplectic geometry. A discipline originated from the geometric objects that describe movement in physics. “I am excited by the unification of different areas of mathematics and the interaction that is achieved by discovering unexpected links,” noted this researcher.
The two specialties in recent years have gained importance in the mathematical world because they were linked to theories of quantum physics, since they explore the most fundamental properties of matter and energy, on a subatomic scale.
Algebraic geometry is a subject that “has a certain rigidity,” as explained by Nigel Hitchin, an English mathematician at the University of Oxford and member of the jury itself. “Modifying, even slightly, the geometric objects in question can cause changes to the point of becoming unrecognizable,” added the expert. Unlike symplectic geometry, which is “more flexible, because from its origins it is studied how position and velocity vary over time,” Hitchin concluded.
The independent work of Claire Voisin and Yakov Eliashberg has made it possible to adapt and relate concepts from both fields, crossing the border between both disciplines. For this reason, “their contributions have broken down barriers and opened new doors in the world of mathematics,” explained the jury. Furthermore, this allows other mathematicians to carry out new research in the future.