Frontiers Award for two mathematicians who joined their fields to understand the subatomic world

The BBVA Foundation Frontiers of Knowledge award in Basic Sciences has been awarded in its latest edition to Claire Voisin, from the National Center for Scientific Research (France) and Yakov Eliashberg, from Stanford University (USA), for promoting the advancement of thought mathematician by breaking down barriers and building bridges between two key areas of geometry.

The award-winning researchers have made outstanding contributions to the so-called algebraic and symplectic geometries, two fields that have acquired special importance in recent years when linked to the theories of quantum physics, which explores the most elementary properties of matter and energy through subatomic scale.

Working independently, mathematicians “have played a fundamental role in the development of these diverse aspects of geometry, in particular by adapting and relating concepts from both fields, crossing the border between both disciplines,” as explained by the jury. .

Voisin and Eliashberg have established parallels between algebraic and symplectic geometry, bringing to light the most flexible aspects of the first and the most rigid of the second, in addition to applying tools from each discipline to study problems in principle assigned to the other.

With these contributions “they have greatly stimulated international research in both areas of mathematics,” concludes the document justifying the award for Voisin, French, and Eliashberg, an American born in Saint Petersburg.

“When the boundaries between two areas of mathematics are broken down, this is very stimulating for researchers in our discipline, since it allows us to adopt a new language and possibly a new framework, a new way of seeing things from the other side, which which allows you to advance further.

If you can frame a challenging problem from another perspective, you can sometimes find a way forward.

This has been a fundamental contribution of Voisin and Eliashberg, who have promoted the progress of mathematics by breaking down barriers between diverse areas of geometry," explained Professor Nigel Hitchin, professor at the University of Oxford (United Kingdom) 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 is used with great success to study particle physics, and which, however, is not completely well defined mathematically.

For this reason, a leading line of research currently consists of trying to reconstruct quantum field theory from symplectic or algebraic geometry and then explore whether the physical consequences deduced from these formulations coincide with reality.

In the previous edition of the award, worth 400,000 euros, the Fronteras went to three physicists, Anne L'Huillier, Paul Corkum and Ferenc Krausz, for observing the attosecond, the equivalent of one trillionth of a second.

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