Lawrence Man Hou Ein (born 18 November 1955) is a mathematician who works in algebraic geometry.
Lawrence Man Hou Ein (born 18 November 1955) is a mathematician who works in algebraic geometry.
Lawrence Ein received in 1976 his bachelor's degree from UCLA [1] and in 1981 his Ph.D. from the University of California, Berkeley under the direction of Robin Hartshorne [2] with thesis Stable vector bundles on projective spaces in char p > 0 (which was published in Mathematische Annalen ). [3] [4]
For the academic year 1981–1982 he was an American Mathematical Society Postdoctoral Research Fellow at the Institute for Advanced Study. From 1982 to 1984 he was a C.L.E. Moore Instructor at MIT. He became from 1984 to 1987 an assistant professor, from 1987 to 1989 an associate professor, and from 1989 to the present a full professor at the University of Illinois at Chicago. He has been a visiting professor at the University of Hong Kong, UCLA, the University of Michigan, Harvard University, the University of Nancy, and the MSRI in Berkeley. [1]
Ein has served on the editorial boards of the Transactions and Memoirs of the American Mathematical Society from 1995 to 2003, Communications in Algebra from 1995 to the present, Geometriae Dedicata from 2004 to 2013, and Serdica Mathematical Journal from 2004 to the present. [1]
Ein was a Sloan Fellow from 1986 to 1989. He was an Invited Speaker of the ICM in 2006 in Madrid. He was elected a Fellow of the American Mathematical Society in 2012. [1]
Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2017. It is named after Takao Fujita, who formulated it in 1985.
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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.
In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant" was coined by Miles Reid (1983) by removing the prefix "dis" from the word "discrepant", to indicate that the resolutions have no discrepancy in the canonical class.
Cameron Leigh Stewart FRSC is a Canadian mathematician. He is a professor of pure mathematics at the University of Waterloo.
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Mihnea Popa is a Romanian-American mathematician at Harvard University, specializing in algebraic geometry. He is known for his work on complex birational geometry, Hodge theory, abelian varieties, and vector bundles.
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In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundle. The theorem states the following
Le Potier (1975): Let X be a n-dimensional compact complex manifold and E a holomorphic vector bundle of rank r over X, here is Dolbeault cohomology group, where denotes the sheaf of holomorphic p-forms on X. If E is an ample, then
from Dolbeault theorem,
By Serre duality, the statements are equivalent to the assertions:
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