David Gregory Ebin

Last updated

David Gregory Ebin (born 24 October 1942, Los Angeles) [1] is an American mathematician, specializing in differential geometry.

Ebin received in 1964 from Harvard University his bachelor's degree and in 1967 his Ph.D. from Massachusetts Institute of Technology under Isadore Singer with thesis On the space of Riemannian metrics. [2] From 1968 to 1969 Ebin was a lecturer at the University of California, Berkeley. He became in 1969 an associate professor and in 1978 a full professor at the Stony Brook University.

Harvard University Private research university in Cambridge, Massachusetts, United States

Harvard University is a private Ivy League research university in Cambridge, Massachusetts, with about 6,700 undergraduate students and about 15,250 postgraduate students. Established in 1636 and named for its first benefactor, clergyman John Harvard, Harvard is the United States' oldest institution of higher learning. Its history, influence, and wealth have made it one of the most prestigious universities in the world.

Massachusetts Institute of Technology University in Massachusetts

The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts. The Institute is a land-grant, sea-grant, and space-grant university, with an urban campus that extends more than a mile (1.6 km) alongside the Charles River. The Institute also encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. It has since played a key role in the development of many aspects of modern science, engineering, mathematics, and technology, and is widely known for its innovation and academic strength, making it one of the most prestigious institutions of higher learning in the world.

Isadore Singer American mathematician

Isadore Manuel Singer is an American mathematician. He is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.

Ebin in the academic years 1983–1984 and 1991–1992 was a visiting professor at UCLA, in 1971 a docent at the École Polytechnique and the University of Paris VII, and in 1976 a member of the Courant Institute in New York. He was elected a Fellow of the American Mathematical Society in 2012.

École Polytechnique

École Polytechnique is a French public institution of higher education and research in Palaiseau, a suburb located south from Paris. It is one of the leading prestigious French 'Grandes Écoles' in engineering, especially known for its polytechnicien engineering program.

American Mathematical Society association of professional mathematicians

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

His research deals with differential geometry, infinite-dimensionalen manifolds (in hydrodynamics and in his treatment of the space of Riemannian metrics), nonlinear partial differential equations, mathematical hydrodynamics (including slightly compressible fluids), and elastodynamics. He investigated in his dissertation the space of Riemannian metrics on a compact manifold and gave this infinite-dimensional space a Riemannian structure.

In 1970 he was, with Jerrold Marsden, an Invited Speaker with talk On the motion of incompressible fluids at the ICM in Nice.

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

Ebin is since 1971 married to Barbara Jean Ebin and has four children.

Selected publications

Jeff Cheeger American mathematician

Jeff Cheeger, is a mathematician. Cheeger is professor at the Courant Institute of Mathematical Sciences at New York University in New York City. His main interests are differential geometry and its connections with topology and analysis.

Related Research Articles

Differential geometry branch of mathematics

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.

Geodesic shortest path between two points on a curved surface

In differential geometry, a geodesic is a curve representing in some sense the shortest path between two points in a surface, or more generally in a Riemannian manifold. It is a generalization of the notion of a "straight line" to a more general setting.

Riemannian geometry branch of differential geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.

Exponential map (Riemannian geometry) in Riemannian geometry

In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold M to M itself. The (pseudo) Riemannian metric determines a canonical affine connection, and the exponential map of the (pseudo) Riemannian manifold is given by the exponential map of this connection.

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a narrow conical piece of a small geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space. As such, it provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n-space. The Ricci tensor is defined on any pseudo-Riemannian manifold, as a trace of the Riemann curvature tensor. Like the metric itself, the Ricci tensor is a symmetric bilinear form on the tangent space of the manifold.

In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.

Mikhail Leonidovich Gromov Russian mathematician

Mikhail Leonidovich Gromov, is an American-French-Russian mathematician known for work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a Professor of Mathematics at New York University.

In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.

In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold is diffeomorphic to a Euclidean space via the exponential map at any point. It was first proved by Hans Carl Friedrich von Mangoldt for surfaces in 1881, and independently by Jacques Hadamard in 1898. Élie Cartan generalized the theorem to Riemannian manifolds in 1928. The theorem was further generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by Ballmann (1990) for metric spaces of non-positive curvature and by Alexander & Bishop (1990) for general locally convex metric spaces.

Robert Bryant (mathematician) American mathematician

Robert Leamon Bryant is an American mathematician and Phillip Griffiths Professor of Mathematics at Duke University. He specializes in differential geometry.

Guofang Wei is a mathematician in the field of differential geometry. She is a professor at University of California, Santa Barbara.

Simon Brendle German mathematician

Simon Brendle is a German mathematician working in differential geometry and nonlinear partial differential equations. He received his Ph.D. from Tübingen University under the supervision of Gerhard Huisken (2001). He was a professor at Stanford University (2005–2016), and is currently a professor at Columbia University. He has held visiting positions at MIT, ETH Zürich, Princeton University, and Cambridge University.

Robert Hermann is an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between vector bundles on Riemannian manifolds and gauge theory in physics, before these interconnections became "common knowledge" among physicists in the 1970s.

Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise Real Reductive Groups.

In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations. These spaces can include singularities and hence catastrophe theory is a part of global analysis. Optimization problems, such as finding geodesics on Riemannian manifolds, can be solved using differential equations so that the calculus of variations overlaps with global analysis. Global analysis finds application in physics in the study of dynamical systems and topological quantum field theory.

José Fernando "Chepe" Escobar was a Colombian mathematician known for his work on differential geometry and partial differential equations. He was professor at Cornell University.

Anthony Joseph Tromba is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.

John "Jack" Marshall Lee is an American mathematician, specializing in differential geometry.

References

  1. ↑ biographical information from American Men and Women of Science, Thomson Gale 2004
  2. ↑ David Gregory Ebin at the Mathematics Genealogy Project
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.