Tuesday, May 10, 2016
4:00 PM -
5:00 PM
Thomas Wolff Memorial Lecture in Mathematics
Lecture 3: New Results on Bounded, Complete Minimal Surfaces
Peter Jones,
Professor,
Mathematics & Applied Math,
Yale University,
Speaker's Bio:
Peter Jones, James E. English Professor of Mathematics and Applied Math at Yale, is a specialist in the field of complex and harmonic analysis, probability theory, and dynamical systems. He came to Yale in 1985 after teaching for six years at the University of Chicago. For several years he lived in Sweden, where he served as assistant director of the Institut Mittag-Leffler. He was the Goran Gustafsson Professor at the Royal Institute of Technology; KTH, in Sweden in 1990. At Yale, he was director of graduate studies in mathematics 1993-95. In 1994, Jones became the youngest person to receive an honorary degree from KTH for his "pathbreaking scientific contributions to modern mathematic analysis" and for promoting the study of mathematics at the institute. He continues to maintain strong ties with the Swedish mathematical community. Jones' other honors include a Sloan Foundation Fellowship, the Salem Prize and a Presidential Young Investigator Award.
Peter Jones, James E. English Professor of Mathematics and Applied Math at Yale, is a specialist in the field of complex and harmonic analysis, probability theory, and dynamical systems. He came to Yale in 1985 after teaching for six years at the University of Chicago. For several years he lived in Sweden, where he served as assistant director of the Institut Mittag-Leffler. He was the Goran Gustafsson Professor at the Royal Institute of Technology; KTH, in Sweden in 1990. At Yale, he was director of graduate studies in mathematics 1993-95. In 1994, Jones became the youngest person to receive an honorary degree from KTH for his "pathbreaking scientific contributions to modern mathematic analysis" and for promoting the study of mathematics at the institute. He continues to maintain strong ties with the Swedish mathematical community. Jones' other honors include a Sloan Foundation Fellowship, the Salem Prize and a Presidential Young Investigator Award.
Abstract: The first example of a bounded, complete minimal surface was given in the 1970's (PJ). Since then several new types of such surfaces have been shown to exist. I will discuss recent research (PJ) showing that there exists a new type of example, namely a complete, bounded Legendrian disk in C^3. This means there are two bounded holomorphic functions (F, G) on the unit disk such that (F(z), G(z),z) is a complete, bounded minimal surface, with the property that (setting H'(z) = F(z)G'(z)) H is also a bounded holomorphic function. The construction uses a modification of Uchiyama's method of decomposing BMO functions into u + H(v), where u and v are bounded functions. I will also discuss some open problems in this area.
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