Lecture Series in Conformal Geometry and Geometric PDE

Lecture 1:

Lecturer: Professor Paul C. Yang, Princeton University, USA (美国普林斯顿大学杨建平教授)

Time: 3:00-4:00pm, Thursday, July 9, 2015

Room: 1124 New Main Building

Title: CR geometry in 3-D

Abstract: In this talk I will explain two ways to choose a canonical contact form on a 3-D CR manifold. Underlying the two approaches is the 4th order operator that contains much information about CR structure in this dimension.

About the Speaker: Professor Paul C. Yang is a Chinese-American mathematician who has made many important contributions in differential geometry and partial differential equations. He is most well known for his work in conformal geometry, his study of extremal metrics and his research on scalar curvature and Q-curvature. Dr. Yang earned his doctorate at the University of California, Berkeley in 1973. He held positions at Rice University, the University of Maryland, Indiana University and the University of Southern California before taking his current position as professor at Princeton University in 2001 Dr. Yang was a Sloan Foundation Fellow in 1981. In 2012, he became a fellow of the American Mathematical Society.


Lecture 2:

Lecturer: Professor Jie Qing, University of California at Santa Cruz (加州大学Santa Cruz分校数学系主任,北京大学长江讲座教授庆杰教授)

Time: 4:00-5:00pm, Thursday, July 9, 2015

Room: 1124 New Main Building Title: Scalar invariants of surfaces in conformal 3-sphere.

Abstract: This is a report for the joint work with Changping Wang and Jingyang Zhong. We are interested in establishing a fundamental theorem for surfaces in conformal 3-sphere and conformal 3-manifolds in general. To do so we regard 3-sphere is the projectivized positive light cone in Minkowski space-time of 5 dimension and, in the same spirit, as the conformal infinity of hyperbolic 4-space. We construct associated surfaces in Minkowski space-time as well as in hyperbolic 4-space and apply fundamental theorem for surfaces in (pseudo)-Riemannian geometry. We are looking to extend the use of ambient spaces of Fefferman and Graham to study the conformal geometry of submanifolds. With this approach, one may produce scalar invariants for surfaces in conformal manifolds.

About the Speaker: Dr. Jie Qing received his Ph.D from the University of California at Los Angeles in 1993. He received an Alfred P. Sloan Research Fellow in 1999. He is currently the Chair of the Department of Mathematics at UCSC. Professor Jie Qing’s research interests include nonlinear analysis, harmonic analysis, and partial differential equations (systems) with applications to differential geometry, complex geometry and mathematical physics. He has made many important contributions in the fields of conformal geometry, geometric problems arising from mathematical relativity. Currently Jie Qing is interested in developing mathematical foundation for AdS/CFT correspondence proposed in the promising theory of quantum gravity in Mathematical Physics.