The Novikov conjecture, groups of diffeomorphisms, and Hilbert-Hadamard spaces

Jianchao Wu 吴健超  (Fudan University)

10:00-11:00, April 21, 2023   Science Building A503

Abstract:

The Novikov conjecture is a prominent problem in differential topology. The operator K-theoretic approach provided by noncommutative geometry has yielded some of the best results that verify this conjecture for vast classes of groups. A natural class of groups for which the conjecture remains largely mysterious is that of countable groups of diffeomorphisms on smooth manifolds. In an upcoming joint paper with Sherry Gong, Zhizhang Xie, and Guoliang Yu, we prove that the (rational strong) Novikov conjecture holds for geometrically discrete countable subgroups of the group of diffeomorphisms of any closed smooth manifold. This removes the volume-preserving condition in a previous joint paper with S. Gong and G. Yu.

About the speaker:

吴健超，复旦大学上海数学中心青年研究员，入选国家级青年人才计划。博士毕业于美国范德堡大学，研究领域为非交换几何和算子代数，在Geom. Funct. Anal.、Adv. Math.、Comm. Math. Phys.、Trans. Amer. Math. Soc.等知名数学期刊发表多篇论文。

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