Henry McKean

Henry P. McKean, Jr. ( born December 14, 1930 in Wenham, Massachusetts ) is an American mathematician who, partial differential equations, mathematical physics and probability theory deals with integrable systems.

Life

McKean studied at Dartmouth College (Bachelor 1972), 1952/53, at the University of Cambridge in England and at Princeton University, where he received his doctorate in 1955 with William Feller (sample functions and stable processes ). From 1955 to 1957 he was instructor at Princeton, in 1957/58 Visiting Professor at Kyoto University and in 1958 at the Massachusetts Institute of Technology (MIT ), where he became a professor. 1963/64, he was a visiting professor at the Rockefeller University, 1964-1966 Professor at MIT, 1966-1970 at The Rockefeller University and from 1970 at the Courant Institute of Mathematical Sciences of New York University, where he 1984-1988 Deputy Director and Chairman the mathematics department, and from 1988 to 1992 was director. 1979/80 he was a visiting professor at Balliol College, Oxford.

He has worked on stochastic processes ( Brownian motion, Markov processes, some with Itō Kiyoshi ), which he applied also early to stock options, models of statistical mechanics ( for example, he showed that the duality of the two-dimensional Ising model consequence of the Poisson summation formula is, J.Math.Physics vol.5, 1964, S.775, work on the Boltzmann equation ) and integrable systems such as the Hill equation ( with van Moerbeke, Trubowitz ), the nonlinear Schrödinger equation or the Korteweg -de Vries equation and its connection with algebraic geometry. With Isadore M. Singer, he also dealt with the relationship of the spectrum of the Laplace operator on manifolds and their curvature ( Curvature and Eigenvalues ​​of the Laplacian Journal of Differential Geometry, Vol.1, 1967, p.43. ) - The work was related influential with index sets.

McKean is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. In 2007 he received for his life's work the Leroy P. Steele Prize. In awarding the prize his textbooks were highlighted. In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Algebraic curves of infinite genus Arising in the theory of nonlinear waves ). He is a Fellow of the American Mathematical Society.

His doctoral include Michael Arbib, Harry Dym, Daniel Stroock, Eugene Trubowitz, Pierre van Moerbeke and Victor Moll.

Writings

  • With Itō Kiyoshi: Diffusion processes and Their sample paths. Springer 1965.
  • Stochastic integral. New York 1969.
  • Harry Dym: Fourier series and integrals. New York 1972.
  • Harry Dym: Stationary Gaussian Processes. New York 1976
  • Harry Dym: Gaussian processes, function theory and the inverse spectral problem-, Academic Press 1976
  • Victor Moll: Elliptic Curves. Cambridge 1997.
Isadore Singer Atiyah–Singer index theorem Name Authority File
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