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Jeffrey B. Rauch (born 29 November 1945, New York City) is an American mathematical physicist, specializing in partial differential equations.
Rauch obtained his bachelor's degree from Harvard University in 1967, and his Ph.D. from New York University in 1971 (with Peter Lax as advisor). [1]
He is a fellow of the American Mathematical Society. [2]
John Forbes Nash, Jr., known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Memorial Prize in Economics. In 2015, he and Louis Nirenberg were awarded the Abel Prize for their contributions to the field of partial differential equations.
Jacques Salomon Hadamard was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations.
Peter David Lax is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.
Lars Valter Hörmander was a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". Hörmander was awarded the Fields Medal in 1962 and the Wolf Prize in 1988. In 2006 he was awarded the Steele Prize for Mathematical Exposition for his four-volume textbook Analysis of Linear Partial Differential Operators, which is considered a foundational work on the subject.
Donald Clayton Spencer was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the University of Colorado and MIT.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Jürgen Kurt Moser was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations.
Luis Ángel Caffarelli is an Argentine-American mathematician. He studies partial differential equations and their applications.
Lawrence Craig Evans is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
Phillip Augustus Griffiths IV is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and distant areas of differential geometry. He also worked on partial differential equations, coauthored with Shiing-Shen Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton.
James Gilbert Glimm is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied mathematics.
Vladimir Gilelevich Maz'ya is a Russian-born Swedish mathematician, hailed as "one of the most distinguished analysts of our time" and as "an outstanding mathematician of worldwide reputation", who strongly influenced the development of mathematical analysis and the theory of partial differential equations.
Neil Sidney Trudinger is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations.
Nassif A. Ghoussoub is a Canadian mathematician working in the fields of non-linear analysis and partial differential equations. He is a Professor of Mathematics and a Distinguished University Scholar at the University of British Columbia.
Avner Friedman is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University. His primary field of research is partial differential equations, with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory.
J. (Jean) François Treves is an American mathematician, specializing in partial differential equations.
Michael Eugene Taylor is an American mathematician, working in partial differential equations.
Maria Elena Schonbek is an Argentine-American mathematician at the University of California, Santa Cruz. Her research concerns fluid dynamics and associated partial differential equations such as the Navier–Stokes equations.
Richard Burt Melrose is an Australian mathematician and professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry.
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