UF Mathematics

Date/Time: Friday, Jan 16th, 2004, Period 7, 1:55-2:45 pm,
Location : CSE Building, Room 119

Abstract:

We describe a way to organize three dimensional computer graphics using methods of differential geometry and algebraic curve theory. From a large set of points in space, we need to compute the geometry of a surface. We proceed by computing the conformal structure of the surfaces and also all the conformal invariants associated with the surfaces. In particular, we compute their period matrices and related holomorphic quadratic differentials. These are used to identify and reconstruct the surfaces. The method is good for recognition registration and data compression; since the parameterization is global, it is also good for the problem of constructing texture.

About the Speaker:

Professor Shing-Tung Yau was awarded a Fields Medal in 1982 for his contributions in the area of geometric partial differential equations, including his solution of the Calabi Conjecture in algebraic geometry, his solution of the Positive Mass Conjecture in general relativity, and his work on real and complex Monge-Ampere equations.

In other work Yau constructed minimal surfaces, studied their stability, and made a deep analysis of how they behave in space-time. His work here has implications for the formation of black holes.

Yau's contributions in minimal surfaces also include an important result on the Plateau problem. This problem was posed by Lagrange in 1760 and was studied by Plateau, Weierstrass, Riemann, and Schwarz, but remained open until being solved independently by Douglas and Rado in the late 1920s. However, there were still questions relating to whether Douglas' solution, which was known to be a smooth immersed surface, is actually embedded. Yau, working with W. H. Meeks, solved this problem in 1980.

In their joint paper "On the existence of Hermitian Yang-Mills connections in stable bundles" (1986), Yau and Karen Uhlenbeck gave a solution of higher-dimensional versions of the Hitchin-Kobayashi conjecture, extending work by Simon Donaldson.

In 1981 Yau was awarded The Oswald Veblen Prize in Geometry, in 1994 the Crafoord Prize of the Royal Swedish Academy of Sciences, and in 1997 the National Medal of Science. He was elected a member of National Academy of Sciences in 1993 and a foreign member of the Russian Academy of Sciences in 2003.

More information can be found at
http://www.cise.ufl.edu/~gu/yau_talk/

Created Wednesday, January 14, 2004.
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Last update made Wed Jan 14 09:51:18 EST 2004.