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Non-degenerate $\mathbb{Z}_2$ harmonic $1$-forms on $\mathbb{R}^n$ and their geometric applications

组织者

河井公大朗 , 钱超 , 唐修棣

演讲者

严大燊

时间

2025年06月13日 16:00 至 17:00

地点

北京理工大学中关村校区研究生教学楼106

线上

Zoom 482 240 1589 (BIMSA)

摘要

The $\mathbb{Z}_2$ harmonic $1$-form arises in various compactification problems in gauge theory, including those involving $PSL(2,\mathbb{C})$ connections and Fueter sections. In this talk, we will describe a recent construction of non-degenerate $\mathbb{Z}_2$ harmonic $1$-forms on $\mathbb{R}^n$ for $n\le 3$, and explore their relation to Lawlor's necks — a family of special Lagrangian submanifolds in $\mathbb{C}^n$. We will also discuss a gluing construction in which these examples are glued to a regular zero of a harmonic $1$-form on a compact manifold. This yields a sequence of non-degenerate $\mathbb{Z}_2$ harmonic $1$-forms whose branching sets shrink to points. As a result, we obtain many new examples of non-degenerate $\mathbb{Z}_2$ harmonic 1-forms on compact manifolds.

The venue is Graduate Teaching Building 106, Zhongguancun Campus, BIT (北京理工大学中关村校区研究生教学楼106). Those wishing to participate should contact Prof. Chao Qian (6120150035@bit.edu.cn) for the entrance permission to the campus.