Euler Characteristic and
Higher Kazhdan Projections
报告专家：Hang Wang (East China Normal University)
报告时间：5月9日（星期五)下午4:00-5:00
报告地点：国家天元数学西南中心516
报告摘要：In this talk, we delve into the interplay between topological invariants and operator algebras by exploring the relationship between the Euler characteristic and higher Kazhdan projections. Focusing on virtually free groups, we demonstrate that the combinatorial Euler characteristic, as introduced by Emerson and Meyer, corresponds to the preimage of the K-theory class of higher Kazhdan projections under the Baum-Connes assembly map. This correspondence allows us to express the K-theory class of higher Kazhdan projections as a finite sum of classes associated with specific averaging projections linked to finite subgroups within the group's Bass-Serre tree structure. An immediate consequence of this framework is the derivation of non-vanishing results for delocalized ℓ²-Betti numbers in this class of groups. Our findings offer insights into the connections between geometric group theory, topology, and operator algebras. This is joint work with Sanaz Pooya and Baiying Ren.
专家简介：王航，华东师范大学算子代数研究中心教授，于2006年本科毕业于复旦大学，2011年博士毕业于美国范德比尔特大学，2011—2013在清华大学丘成桐数学科学中心做博士后。2013—2017在澳大利亚阿德莱德大学工作。研究方向是非交换几何以及椭圆算子的指标理论，属泛函分析。她有多篇代表性论文发表在一流数学期刊上，如：Journal of Differential Geometry, Advances in Mathematics, Proceedings of the London Mathematical Society等。曾入选海外高层次青年人才计划。
邀请人：Rodsphon Rudy
