Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional geometric topology (specifically of 4-manifolds) and the mathematics of gauge theory.
Fintushel studied mathematics at Columbia University with a bachelor's degree in 1967 and at the University of Illinois at Urbana–Champaign with a master's degree in 1969. [1] In 1975 he received his Ph.D. from the State University of New York at Binghamton with thesis Orbit maps of local -actions on manifolds of dimension less than five under the supervision of Louis McAuley. [2] Fintushel was a professor at Tulane University and is a professor at Michigan State University.
His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with links to gauge theory, knot theory, and symplectic geometry. He works closely with Ronald J. Stern.
In 1998 he was an Invited Speaker, with Ronald J. Stern, with talk Construction of smooth 4-manifolds at the International Congress of Mathematicians in Berlin. [3] In 1997 Fintushel received the Distinguished Faculty Award from Michigan State University. In 2016 a conference was held in his honor at Tulane University. [4]
He was elected a Fellow of the American Mathematical Society. Fintushel is a member of the editorial boards of Geometry & Topology and the Michigan Mathematical Journal .
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution may be given as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions are opposite to two equivalent conditions for 'complete integrability' of a hyperplane distribution, i.e. that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem.
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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.
In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds which admit no smooth structure, and even if there exists a smooth structure, it need not be unique.
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.
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The Geometry Festival is an annual mathematics conference held in the United States.
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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.
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Denis Auroux is a French mathematician working in geometry and topology.