The last Kervaire invariant problem

Time：Friday, 16:00-17:00 Dec. 6, 2024

Venue：Zoom Meeting ID 271 534 5558 Passcode: YMSC

Speaker：Guozhen Wang

Time

Friday, 16:00-17:00

Dec. 6, 2024

Online

Zoom Meeting ID

271 534 5558

Passcode: YMSC

/ 主讲人

Speaker /

Guozhen Wang 王国祯

Fudan University

王国祯，复旦大学上海数学中心及数学科学学院双聘教授、博士生导师。主要从事同伦论相关方向的研究，在球面同伦群、球面上微分结构分类、母体同伦论、等变同伦论、拓扑循环同调的研究上取得重要研究成果，发表在Ann. Math., Acta Math., Invent. Math. 等期刊上。获得国家自然基金杰出青年项目。

/ 讲座简介

About the lecture /

The last Kervaire invariant problem

Abstract

The Kervaire invariant problem asks in which dimensions there exits framed manifolds of Kervaire invariant one. This has many implications in geometry and topology, such as the classification of homotopy spheres. By efforts of Browder, Barratt, Jones, Mahowald, Tangora, Hill, Hopkins, Ravenel, we know the answers in dimensions other than 126. Recently, joint with Weinan Lin and Zhouli Xu, we show that there exists Kervaire invariant one manifolds in dimension126. Hence we can conclude that the only dimensions admitting framed manifolds of Kervaire invariant one are 2, 6, 14, 30, 62 and 126.

DATEDecember 4, 2024

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