Foliation Divisorial Contraction by the Sasaki-Ricci Flow in a Sasakian Manifold of Dimension Five

发布时间：2023-12-05 作者：浏览次数：

Speaker:	张树城	DateTime:	2023年12月14日（周四）下午3:00-4:00
Brief Introduction to Speaker: 张树城教授为重庆理工大学数学科学研究中心特聘教授。1990年毕业于美国莱斯大学，1990年-2007年担任台湾清华大学数学系副教授、教授，期间于2003年-2007年担任国立清华大学数学系主任；2008年-2022 年担任台湾大学数学系教授。从2008年起担任台湾大学数学科学中心几何分析顶尖研究计划主持人，投入顶尖研究及培育了多位杰出博士生。从事微分几何及几何分析的研究工作，在 JDG, Math. Ann., Crelle's, IMRN, CAG, Calc. Var. PDE, Trans. AMS, IUMJ, JGA, Math. Z. 等杰出数学期刊发表科学论文70余篇; 因在柯西-黎曼几何与佐佐木几何的杰出研究, 于2015年荣获台湾数学会学术奖殊荣。		Place:	六号楼二楼报告厅
Abstract:A Sasakian (2n+1)-manifold is served as the odd-dimensional analogous of Kaehler manifolds. For instance, the Kaehler cone of a Sasaki-Einstein 5-manifold is a Calabi-Yau 3-fold. On the other hand, the class of simply connected, closed, oriented, smooth 5-manifolds is classifiable under diffeomorphism due to Smale-Barden. In this talk, we consider a compact quasi-regular Sasakian 5-manifold with finite cyclic quotient foliation singularities of type (1/r)(1,a). We first derive the foliation Blow-up and Sasaki Castelnuovo's Contraction Theorem. Secondly, based on the the foliation canonical surgical contraction and extremal ray contraction under the Sasaki-Ricci flow, we prove a Sasaki analogue of analytic minimal model program via the Kaehler-Ricci flow due to Song-Tian and Song-Weinkove. This is a joint work with C. Lin and C.-T. Wu.

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