几何与拓扑讨论班——Chromatic redshift and Segal conjecture

报告人：Rixin Fang，Fudan University

Pretalk

主题：Introduction to K-theory and Hochschild Homology

时间：2025年4月28日，16:15-16:45

摘要：We introduce low dimensional K-theory first, and briefly explain Quillen's plus construction. Then we recall the Hochschild homology of an algebra, and its relation with K-theory. If time permits, we give a briefly introduction on stable homotopy theory, and $v_n$-periodicity.

Research Talk

主题：Chromatic redshift and Segal conjecture

时间：2025年4月28日，16:45-17:35

摘要：The Lichtenbaum--Quillen property comes with an arithmetic background, Waldhausen reformulated this property as a telescopic homotopy problem. The chromatic redshift introduced by Rognes generalized this idea to higher height ring spectra. And algebraic K-theory for ring spectra can be well understood by trace method, we will briefly recall the trace method. By the work of J. Hahn, D. Wilson, et al., the redshift problem can be reduced to Segal conjecture and (weak) canonical vanishing problem. We recall the techniques to prove Segal conjecture, and we present examples that Segal conjecture holds. We use the cyclic decomposition to demonstrate some examples that Segal conjecture fails, and thus Lichtenbaum--Quillen property fails also.

地点：紫金港校区海纳苑2幢204室

组织者：Hana Jia Kong, Song Sun,

              Lei Wu, Weiwei Wu