中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：谢羿（北京大学）   

题  目：Configuration space integral, graph cohomology and the diffeomorphism groups of 4-manifolds

时  间：2023.10.25（星期三）14:30-16:30

地  点： 数学院南楼N 802

摘  要：In 2018, Watanabe used a version of configuration space  integral to detect non-trivial smooth families of disk bundles and disproved the 4-dimensional Smale conjecture. More precisely, he related the homotopy groups of Diff(D^4) to the so called graph cohomology. In this talk we will show that the configuration space integral only depends the formal smooth structure, i.e. a lift of the tangent microbundle to a vector bundle. As an application, we can generalize Watanabe’s result and obtain information on the diffeomorphism group of a general compact oriented 4-manifold in terms of the graph cohomology. This is joint work with Jianfeng Lin.

=================================

报告人：袁天宇（北京大学）   

题  目：A link invariant from higher-dimensional Heegaard Floer homology

时  间：2023.11.01（星期三）14:00-15:00

地  点：数学院南楼N 802

摘  要：We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a k-strand braid, which is expressed as an element of the symplectic mapping class group. We then apply the higher-dimensional Heegaard Floer homology machinery to this element. We prove its invariance under arc slides and Markov stabilizations, which shows that it is a link invariant.

个人简介：袁天宇，北京大学博士后，博士毕业于加州大学洛杉矶分校，研究方向为低维拓扑与辛几何。