报告1
报告题目：Inverse curvature flow and some geometric applications
报告时间：2018年7月5日（星期四）09:00—09:45
报告地点：苏州大学本部精正楼211
报告人：Haizhong Li (Tsinghua University)
报告提要：In this talk, we give some important properties of inverse curvature flows for hypersurfaces in a space form or in some warped Riemanniann manifolds. By use of the properties of inverse curvature flows, we prove some geometric inequalities for such hypersurfaces.
报告2
报告题目：Volume entropy rigidy for RCD spaces
报告时间：2018年7月5日（星期四）10:15—10:00
报告地点：苏州大学本部精正楼211
报告人：Xianzhe Dai (UC Santa Barbara)
报告提要：Volume entropy is a fundamental geometric invariant defined as the exponential growth rate of volumes of balls in the universal cover. It is a very subtle invariant which has been extensive studied in geometry, topology and dynamical systems. RCD spaces are the most general metric spaces which one can still talk about Ricci curvature lower bounds (and still in the Riemannian category). They contain the Ricci limit spaces and has attracted intensive attentions recently. We will report some of our recent joint work with Chris Connell, Jesus Nunez-Zimbron, Requel Perales, Pablo Suarez-Serrato and Guofang Wei about the generalization to RCD spaces of the volume entropy rigidity results, including that of Ledrappier and Wang which says that for a compact Riemannian manifold whose Ricci curvature is bounded from below by –(n–1), then the volume entropy is bounded from above by (n–1) and the equality holds iff the manifold is hyperbolic.
报告3
报告题目：Harmonic maps and singularities of period mappings
报告时间：2018年7月5日（星期四）11:10—11:55
报告地点：苏州大学本部精正楼211
报告人：Yihu Yang (Shanghai Jiao Tong University)
报告提要：We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. This is a joint work with J. Jost and K. Zuo.
报告4
报告题目：Length-constrained curve diffusion
报告时间：2018年7月5日（星期四）14:00—14:45
报告地点：苏州大学本部精正楼211
报告人：James McCoy (The University of Newcastle)
报告提要：The curve diffusion flow has the fundamental property that for closed curves in the plane the signed enclosed area is constant under the flow. It is natural to consider a ‘dual’ fourth order flow that instead preserves length under the evolution. We introduce such a flow and show that initial closed curves of winding number one, whose oscillation of curvature is suitably small and whose isoperimetric ratio is close enough to one, produce solutions to the flow that exist for all time and converge exponentially to a round circle. This is joint work with Glen Wheeler and Yuhan Wu.
报告5
报告题目：Generalized Strichartz estimates for Schrodinger type equations and applications
报告时间：2018年7月5日（星期四）09:00—09:45
报告地点：苏州大学本部精正楼211
报告人：Zihua Guo (Monash University)
报告提要：In this talk we give a survey on the recent studies for the generalized Strichartz estimates for Schrodinger type equations and their applications to the nonlinear dispersive equations/systems. The generalized Strichartz estimates include: almost sharp estimates in the radial case or spherically averaged case, and for Schrodinger equations with potential; the applications include: Klein-Gordon equation, Zakharov system, Gross-Pitaevskii equation.
报告6
报告题目：Eigenvalues of Riemannian manifolds admitting large symmetry
报告时间：2018年7月5日（星期四）16:10—16:55
报告地点：苏州大学本部精正楼211
报告人：Zuoqin Wang (University of Science and Technology of China)
报告提要：Let M be a compact Riemannian manifold on which a compact Lie group acts by isometries. In this talk I will explain how the symmetry induces extra structures in the spectrum of Laplace-type operators, and how to apply symplectic techniques to study the induced equivariant spectrum. This is based on joint works with V. Guillemin and with Y. Qin.
报告7
报告题目：Volume preserving flow and Alexandrov-Fenchel inequalities in hyperbolic space
报告时间：2018年7月5日（星期四）17:05—17:50
报告地点：苏州大学本部精正楼211
报告人：Yong Wei (Australian National University)
报告提要：I will describe my recent work with Ben Andrews and Xuzhong Chen on volume preserving flow and Alexandrov-Fenchel inequalities in hyperbolic space. If the initial hypersurface in hyperbolic space has positive sectional curvature, we show that a large class of volume preserving flows preserve the positivity of sectional curvatures, and the evolving hypersurfaces converge smoothly to a geodesic sphere. This result can be used to show that certain Alexandrov-Fenchel quermassintegral inequalities, known previously for horospherical convex hypersurfaces, also hold under the weaker condition of positive sectional curvature.