The CUNY graduate center building is 365 5th Avenue (34th St) in Manhattan. Just a 10 minute cab ride from NYU (remember you can split the cab fare), or take the Broadway subway line (R from 8th to 34th). The first talk at the Geometry Festival is at 3pm. Please bring your university ID with you and sign in at the front desk. No registration necessary. Please contact Christina Sormani if you have any questions. Tea and coffee will be available in Room 4214 between talks.
We give a new global criterion for warped products of metric spaces to have a given curvature bound above or below. This construction extends the known criterion for linear cones, by replacing the radial coordinate with elements of a rich class of generalized convex functions on metric spaces. The proof considers the propagation of curvature bounds, and the geometry of vertex sets (vanishing points of the warping function). In addition to extending coning from 1 dimensional to arbitrary base, the construction generalizes standard gluing theorems from 0 dimensional to arbitrary fibre.
In this talk, we will explore the relation between the algebraic canonical degeneration of family of algebraic manifolds and the convergence of the corresponding family of Kahler-Einstein manifolds in sense of Cheeger-Gromov. As application, we will discuss the convergence and degeneration of complete Kahler-Einstein hypersurfaces in multi-dimension complex tori. We will also discuss geometric representation of vanishing cycles of degeneration as "minimal submanifolds".
Abstract: We show the existence of harmonic functions on certain manifolds with nonnegative Ricci curvature. Roughly speaking, this is to solve a Dirichlet problem at the space infinity.