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BIMSA-BIT Differential Geometry Seminar
Non-degenerate $\mathbb{Z}_2$ harmonic $1$-forms on $\mathbb{R}^n$ and their geometric applications
Non-degenerate $\mathbb{Z}_2$ harmonic $1$-forms on $\mathbb{R}^n$ and their geometric applications
Organizers
Kotaro Kawai
, Chao Qian
, Xiudi Tang
Speaker
Dashen Yan
Time
Friday, June 13, 2025 4:00 PM - 5:00 PM
Venue
北京理工大学中关村校区研究生教学楼106
Online
Zoom 482 240 1589
(BIMSA)
Abstract
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.