The BBVA Foundation Frontiers of Knowledge Award in Basic Sciences, in its latest edition, was awarded to Claire Voisin from the National Center for Scientific Research (France) and Yakov Eliashberg from Stanford University (USA) for promoting the further development of the thought mathematician, breaking down barriers and bridging between build two key areas of geometry.
The award-winning researchers have made outstanding contributions to the so-called algebraic and symplectic geometries, two areas that have gained particular importance in recent years by linking them to the theories of quantum physics, which explores the most elementary properties of matter and energy through methods at the subatomic scale .
In their independent work, mathematicians have “played a fundamental role in the development of these diverse aspects of geometry, particularly by adapting and combining concepts from both fields and by crossing the boundary between the two disciplines,” the jury said. Voisin and Eliashberg have established parallels between algebraic and symplectic geometry, bringing to light the most flexible aspects of the former and the most rigid aspects of the latter, in addition to applying tools from both disciplines to investigate principally problems associated with the other. With these contributions “they have significantly stimulated international research in both areas of mathematics,” says the document justifying the award to Voisin, a Frenchman, and Eliashberg, an American born in St. Petersburg.
“When the boundaries between two areas of mathematics are erased, it is very stimulating for researchers in our discipline because it allows us to adopt a new language and perhaps a new framework, a new way of looking at things from the other side.” which allows you to move forward. If you can look at a challenging problem from a different perspective, you can sometimes find a way forward. “This was a fundamental contribution by Voisin and Eliashberg, who advanced the progress of mathematics by breaking down barriers between different areas of geometry,” said Professor Nigel Hitchin, Professor at the University of Oxford (UK) and member of the jury.
Today, both symplectic and algebraic geometry have gained renewed importance due to their potential to provide mathematical foundations for quantum field theory. This is a branch of quantum physics that has been used with great success to study particle physics, but is not fully defined mathematically. For this reason, a leading research direction currently is to reconstruct quantum field theory from symplectic or algebraic geometry and then examine whether the physical consequences derived from these formulations are consistent with reality.
In the previous edition of the 400,000 euro prize, the Fronteras went to the three physicists Anne L'Huillier, Paul Corkum and Ferenc Krausz for the observation of the attosecond, the equivalent of a trillionth of a second.
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