In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its diffeomorphism group. Because many of these coarser properties may be captured algebraically, differential topology has strong links to algebraic topology.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
Sergei Petrovich Novikov was a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. He became the first Soviet mathematician to receive the Fields Medal in 1970.
Richard Streit Hamilton is an American mathematician who serves as the Davies Professor of Mathematics at Columbia University. He is known for contributions to geometric analysis and partial differential equations. Hamilton is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. However, Perelman declined the award, regarding Hamilton's contribution as being equal to his own.
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is now worth US$5000, and is awarded every three years.
In mathematics, specifically geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence should imply a stronger, topological notion.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University.
The Geometry Festival is an annual mathematics conference held in the United States.
The mathematician Shmuel Aaron Weinberger is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was, from 1994 to 1996, the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, and he is currently the Andrew MacLeish Professor of Mathematics and chair of the Mathematics department at the University of Chicago.
James W. Cannon is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He was an Orson Pratt Professor of Mathematics at Brigham Young University.
Wolfgang Lück is a German mathematician who is an internationally recognized expert in algebraic topology.
Lowell Edwin Jones is an American professor of mathematics at Stony Brook University. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with F. Thomas Farrell on the Farrell-Jones conjecture.
Wu-Chung Hsiang is a Taiwanese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.
Kaoru Ono is a Japanese mathematician, specializing in symplectic geometry. He is a professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University.
Arthur Bartels is a German mathematician.
Michael W. Davis is an American mathematician, author and academic. He is a Professor Emeritus of mathematics at the Ohio State University.
Pedro Ontaneda Portal is a Peruvian-American mathematician specializing in topology. He is a distinguished professor at Binghamton University, a unit of the State University of New York. He received his Ph.D. in 1994 from Stony Brook University, advised by Lowell Jones; subsequently he taught at the Federal University of Pernambuco in Brazil before moving to Binghamton.
