Denis Auroux | |
|---|---|
 Professor Auroux in 2010 | |
| Born | April 1977 (age 47) |
| Nationality | French |
| Alma mater | École normale supérieure Paris Diderot University Pierre and Marie Curie University Paris-Sud University École polytechnique |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Massachusetts Institute of Technology University of California, Berkeley Harvard University |
Denis Auroux (born April 1977) [1] is a French mathematician working in geometry and topology.
Auroux was admitted in 1993 to the École normale supérieure. In 1994, he received a licentiate and maîtrise in mathematics from Paris Diderot University (Paris 7). In 1995, he received a licentiate in physics from Pierre and Marie Curie University (Paris 6) and passed the agrégation . In 1995, he received a master's degree in mathematics from Paris-Sud University with a thesis on Seiberg-Witten invariants of symplectic manifolds. In 1999, he received his doctorate from the École polytechnique with supervisors Jean-Pierre Bourguignon and Mikhael Gromov for a thesis on structure theorems for compact symplectic manifolds via almost-complex techniques. In 2003, he completed his habilitation at Paris-Sud University with a thesis on approximately holomorphic techniques and monodromy invariants in symplectic topology.
As a postdoc, he was a C. L. E. Moore Instructor at the Massachusetts Institute of Technology from 1999 to 2002, where he became an assistant professor in 2002, an associate professor in 2004 (tenured in 2006), and a professor in 2009 (on leave from 2009 to 2011). From 2009 to 2018, he was a professor at the University of California, Berkeley. Since Fall 2018, he has been at Harvard University, [2] where he taught Math 55, two-semester honors undergraduate course on algebra and analysis. [3]
His research deals with symplectic geometry, low-dimensional topology, and mirror symmetry. [4] [5]
In 2002, he received the Prix Peccot from the Collège de France. In 2005, he received a Sloan Research Fellowship. [2] He was an invited speaker in 2010 with talk Fukaya Categories and bordered Heegaard-Floer Homology [6] at the International Congress of Mathematicians in Hyderabad and in 2004 at the European Congress of Mathematicians in Stockholm. [7]
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called symplectic Floer homology, in his proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as (smooth) three- and four-dimensional manifolds.
Clifford Henry Taubes is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taubes.
Alexander Givental is a Russian-American mathematician who is currently Professor of Mathematics at the University of California, Berkeley. His main contributions have been in symplectic topology and singularity theory, as well as their relation to topological string theories.
Yakov Matveevich Eliashberg is an American mathematician who was born in Leningrad, USSR.
Danny Matthew Cornelius Calegari is a mathematician and, as of 2023, a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory.
Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.
Kenji Fukaya is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the Fukaya category. He is a permanent faculty member at the Simons Center for Geometry and Physics and a professor of mathematics at Stony Brook University.
Bernd Siebert is a German mathematician who researches in algebraic geometry.
Victor Vadimovich Batyrev is a Russian mathematician, specializing in algebraic and arithmetic geometry and its applications to mathematical physics. He is a professor at the University of Tübingen.
This is a glossary of properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry. The glossary also includes notions from Hamiltonian geometry, Poisson geometry and geometric quantization.
François Lalonde is a Canadian mathematician, specializing in symplectic geometry and symplectic topology.
Kaoru Ono is a Japanese mathematician, specializing in symplectic geometry. He is a professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University.
Ivan Smith is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge.
Serguei Barannikov is a mathematician, known for his works in algebraic topology, algebraic geometry and mathematical physics.
Yongbin Ruan is a Chinese mathematician, specializing in algebraic geometry, differential geometry, and symplectic geometry with applications to string theory.
Ronald Alan Fintushel is an American mathematician, specializing in low-dimensional geometric topology and the mathematics of gauge theory.
Dmitri Olegovich Orlov, is a Russian mathematician, specializing in algebraic geometry. He is known for the Bondal-Orlov reconstruction theorem (2001).
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
