John W. Morgan
Columbia University
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2009)
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Research Interests
Professor Morgan's work has always been at the interface of Topology and other areas of mathematics such as Differential Geometrty, Algebratic Geometry and Mathematical Physics. His most recent work has concerned spaces of dimensions 3 and 4 where the interplay between analysis, geometry and mathematical physics is especially rich. For example, he has studied extensively gauge theory invariants, originally arising in Mathematical Physics, and in particular their use in the study of 4-dimensional spaces, especially complex algebraic surfaces. He has also studied a geometric PDE evolution equation, Ricci Flow, and its application to the topology of 3-dimensional spaces, one consequence of this study being the resolution of the Poincare Conjecture characterizing the 3-dimensional sphere.
