16:00 - 17:00, September 2, 2025 (Tuesday) Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)
Moduli Spaces of Instantons on Asymptotically Conical Spin(7)-Manifolds Tathagata Ghosh (NCTS)
Abstract
In this talk we discuss instantons on asymptotically conical Spin(7)-manifolds where the instanton is asymptotic to a fixed nearly G2-instanton at infinity. After discussing the preliminary notions of G2 & Spin(7)-manifolds, asymptotically conical manifolds, and Yang-Mills equations & instantons, we mainly focus on the deformation theory of AC Spin(7)-instantons by relating the deformation complex with Dirac operators and spinors, and applying spinorial methods to identify the space of infinitesimal deformations with the kernel of a twisted negative Dirac operator on the asymptotically conical Spin(7)-manifold.
As examples, we consider two important Spin(7) manifolds: , where is considered to be an asymptotically conical manifold asymptotic to the cone over the round 7-sphere, and Bryant-Salamon manifold - the negative spinor bundle over 4-sphere, asymptotic to the cone over the squashed 7-sphere. We apply the deformation theory to describe deformations of Fairlie-Nuyts-Fubini-Nicolai (FNFN) Spin(7)-instantons on , and the Clarke-Oliviera instanton on the negative spinor bundle over 4-sphere. We also calculate the virtual dimensions of the moduli spaces using Atiyah-Patodi-Singer index theorem and the spectrum of the twisted Dirac operators.
If time permits, I will give an overview of my current work in understanding the moduli spaces better, which is based on joint work with D. Harland.
