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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.
Andreas Floer was a German mathematician who made seminal contributions to symplectic topology, and mathematical physics, in particular the invention of Floer homology. Floer's first pivotal contribution was a solution of a special case of Arnold's conjecture on fixed points of a symplectomorphism. Because of his work on Arnold's conjecture and his development of instanton homology, he achieved wide recognition and was invited as a plenary speaker for the International Congress of Mathematicians held in Kyoto in August 1990. He received a Sloan Fellowship in 1989.
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten.
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.
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The Geometry Festival is an annual mathematics conference held in the United States.
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In symplectic topology, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Lagrangian Floer chain groups: . Its finer structure can be described as an A∞-category.
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.
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.
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.
Dietmar Arno Salamon is a German mathematician.
Denis Auroux is a French mathematician working in geometry and topology.
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry.
References
- ↑ Ivan Smith at the Mathematics Genealogy Project
- ↑ Whitehead Prize to Smith 2007
- ↑ "Ivan Smith". royalsociety.org. Retrieved 25 May 2023.
