Theodore James "Ted" Courant is an American mathematician who has conducted research in the fields of differential geometry and classical mechanics. In particular, he made seminal contributions to the study of Dirac manifolds, [1] [2] which generalize both symplectic manifolds and Poisson manifolds, and are related to the Dirac theory of constraints in physics. Some mathematical objects in this field have since been named after him, including the Courant bracket and Courant algebroid.
Courant received his B.A. degree from Reed College, [3] and his Ph.D. from The University of California, Berkeley, where he was a student of Alan Weinstein. [4]
After teaching at the University of California, Santa Cruz and the University of Minnesota, Courant moved to secondary education at private schools in California including The Branson School and Wildwood School. [3]
Ted Courant is the grandson of Richard Courant. [5]
Paul Adrien Maurice Dirac was an English mathematical and theoretical physicist who is considered to be one of the founders of quantum mechanics and quantum electrodynamics. He is credited with laying the foundations of quantum field theory. He was the Lucasian Professor of Mathematics at the University of Cambridge, a professor of physics at Florida State University and the University of Miami, and a 1933 Nobel Prize in Physics recipient.
Maxim Lvovich Kontsevich is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Breakthrough Prize in Fundamental Physics in 2012, and the Breakthrough Prize in Mathematics in 2015.
Shiing-Shen Chern was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics."
Mikhael Leonidovich Gromov is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of Institut des Hautes Études Scientifiques in France and a professor of mathematics at New York University.
In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics.
Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
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.
André Lichnerowicz was a French differential geometer and mathematical physicist. He is considered the founder of modern Poisson geometry.
Richard Melvin Schoen is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984.
Jerrold Eldon Marsden was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.
In a field of mathematics known as differential geometry, the Courant bracket is a generalization of the Lie bracket from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of p-forms.
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.
Alan David Weinstein is a professor of mathematics at the University of California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry.
In a field of mathematics known as differential geometry, a Courant geometry was originally introduced by Zhang-Ju Liu, Alan Weinstein and Ping Xu in their investigation of doubles of Lie bialgebroids in 1997. Liu, Weinstein and Xu named it after Courant, who had implicitly devised earlier in 1990 the standard prototype of Courant algebroid through his discovery of a skew symmetric bracket on , called Courant bracket today, which fails to satisfy the Jacobi identity. Both this standard example and the double of a Lie bialgebra are special instances of Courant algebroids.
Charles L. Epstein is a Senior Research Scientist in the Center for Computational Mathematics at the Flatiron Institute. He is the Thomas A. Scott Professor of Mathematics Emeritus at the University of Pennsylvania, Philadelphia.
Theodore Frankel was a mathematician who introduced the Andreotti–Frankel theorem and the Frankel conjecture.
In mathematics a Dirac structure is a geometric construction generalizing both symplectic structures and Poisson structures, and having several applications to mechanics. It is based on the notion of the Dirac bracket constraint introduced by Paul Dirac and was first introduced by Ted Courant and Alan Weinstein.
A Lie bialgebroid is a mathematical structure in the area of non-Riemannian differential geometry. In brief a Lie bialgebroid consists of two compatible Lie algebroids defined on dual vector bundles. They form the vector bundle version of a Lie bialgebra.
Viktor L. Ginzburg is a Russian-American mathematician who has worked on Hamiltonian dynamics and symplectic and Poisson geometry. As of 2017, Ginzburg is Professor of Mathematics at the University of California, Santa Cruz.
Alberto Sergio Cattaneo is an Italian mathematician and mathematical physicist, specializing in geometry related to quantum field theory and string theory.