Geometry & Analysis Seminar Winter 2017
McHenry Room 4130
For further information please contact Professor Longzhi Lin or call 831-459-2400
January 12, 2017
January 19, 2017
Title: Minimizing Trajectories and the Hamilton Jacobi Equation
Abstract: The classical Hamilton-Jacobi theory was always known to be related to the study of minimizers of the action. The subject was almost forgotten, due to the lack of classical solutions of the H-J equation, until it reappeared with the weak KAM theory of Fathi. I will discuss the modern approach to that classical relation.
January 26, 2017
February 2, 2017
February 9, 2017
Lihan Wang, University of California, Irvine
Title: " Symplectic Laplacians, Boundary Conditions and Cohomology"
Abstract: Tseng and Yau introduce so-called symplectic Laplacians in 2012 in the studio super-symmetry. In this talk, we will discuss these Laplacians and their relations with cohomologies on compact manifolds with boundary. For this purpose, new conditions, so -called symplectic boundary conditions, on forms are also introduced in this talk.
February 16, 2017
February 23, 2017
Title: The Dimension of the Boundary of the Developing Image
Abstract: Suppose Ω is a domain on the standard sphere (Sn,g0), n≥3. And g=u4/(n-2)g0 is a complete conformal metric on Ω. Curvature conditions imposed on g will give restriction to the Hausdorff dimension of the boundary ∂Ω. In this talk, I will give a survey on several classical results and state some new results.
March 3, 2017
Zheng Huang, Graduate Center and City University of New York, Staten Island
Title: Closed Minimal Surfaces in Some Hyperbolic Three-manifolds (and Where to Find Them)
Abstract: I will present main ideas in proving some recent results on finding closed immersed incompressible minimal surfaces in several classes of hyperbolic three-manifolds. Much of this is based on joint work with B. Wang.
March 9, 2017
Xiaolong Li, University of California, San Diego
Title: Four-dimensional Shrinking Solitons with Positive Isotropic Curvature
Abstract: In this talk, I will present a classification result: a four-dimensional complete gradient shrinking Ricci soliton with positive isotropic curvature is either a quotient of S4 or a quotient of S3 • R. This is joint work with Lei Ni and Kui Wang.
March 16, 2017
*Special time: 3-4pm*
Hongnian Huang, University of New Mexico