中科院数学与系统科学研究院

数学研究所

数学物理研讨班

报告人： Prof. Han Qing（University of Notre Dame/Peking University）

题  目：Nonexistence of Poincare-Einstein Fillings on Spin Manifolds

时  间：2017.12.18（星期一），10:00-11:00

地  点：数学院南楼N913室

摘  要：Graham and Fefferman raised the question whether a conformal class on the boundary M of a given compact manifold X can be the conformal infinity of a Poincare-Einstein metric in X. In this talk, we construct an invariant of conformal classes on the boundary M of a compact spin manifold X of dimension 4k with the help of the Dirac operator. We prove that a conformal class cannot be the conformal infinity of a Poincare-Einstein metric if this invariant is not zero. Furthermore, we will prove this invariant can attain values of infinitely many integers if one invariant is not zero on the above given spin manifold. This talk is based on a joint work with Gursky and Stolz.