The coarse Baum-Connes conjecture for product metric spaces

Jianguo Zhang 张建国  (Shaanxi Normal University)

14:00-15:00, November 13, 2024   Tencent Meeting ID: 790 559 344 (Passcode: 920146)

Abstract:

The coarse Baum-Connes conjecture asserts that the higher index map from the coarse $K$-homology of a metric space $X$ to the $K$-theory of the Roe algebra of $X$ is an isomorphism. The conjecture has its roots in the celebrated Atiyah-Singer index theorem and has significant applications to topology and geometry, such as the Novikov conjecture and Gromov-Lawson-Rosenberg conjecture. A natural question is whether the conjecture is closed under products. In this talk, we will answer this question by introducing a notion called the Roe algebra with filtered coefficients which is inspired by Yu’s quantitative $K$-theory.

About the speaker:

张建国，陕西师范大学数学与统计学院讲师，2020年博士毕业于复旦大学，之后在华东师范大学做博士后，研究方向是算子代数与非交换几何，在粗Baum-Connes猜想方面取得一些结果，相关成果发表在Commun. Math. Phys., J. Noncommut. Geom.等期刊上。

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