报告方式：线上报告，腾讯会议（ID：950 605 092）
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//meeting.tencent.com/s/cgC5qjnsYILG
线下地点：行健楼学术活动室526
邀请人：何跃副教授
摘要： Ancient solutions are important in studying singularities of mean curvature flows (MCF). So far most rigidity results about ancient solutions are modeled on shrinking spheres or spherical caps. In this talk, I will describe the behavior of MCF for a class of submanifolds, called isoparametric submanifolds, which have more complicated topological type. We can show that all such solutions are in fact ancient solutions, i.e. they exist for all time which goes to negative infinity. Similar results also hold for MCF of regular leaves of polar foliations in simply connected symmetric spaces with non-negative curvature. I will also describe our conjectures proposed together with Terng on rigidity of ancient solutions to MCF for hypersurfaces in spheres. These conjectures are closely related to Chern’s conjecture for minimal hypersurfaces in spheres. This talk is based on joint works with Chuu-Lian Terng and Marco Radeschi.
报告人简介：刘小博教授，本科毕业于清华大学，博士毕业于美国宾夕法尼亚大学，曾任美国圣母大学教授，2015年全职回国，在北京国际数学中心工作。他曾在《Annals of Math.》、《Duke Math. Journal》、《Journal of Differential Geometry》、《Math. Ann.》、《Trans. Amer. Math. Soc. 》、《Comm. Math. Phys.》、《Amer. J. Math.》等国际一流期刊上发表多篇论文。由于他在几何与数学物理领域杰出的学术成就，曾获得美国 Sloan 研究奖，并于2006年应邀在西班牙马德里召开的国际数学家大会上作特邀报告（45分钟）。目前，他担任北京大学讲席教授、北京国际数学中心的副主任，以及Peking Mathematical Journal 的主编等职务。主要研究领域和专长：微分几何、辛几何和数学物理。主要研究方向： Gromov-Witten不变量普适方程和Virasoro猜想、等参子流形、整体极小子流形等。