[Mini Courses] Introduction to Donaldson Theory
时间 Datetime
2024-03-18 14:00 — 15:30
地点 Venue
会议室(706)
报告人 Speaker
马烺特
邀请人 Host
来米加
备注 remarks
报告摘要 Abstract
This is a 4-lecture minicourse on Donaldson theory.
Lecture 1.Yang-Mills Equations
I will start by introducing two basic questions in 4-dimensional topology to motivate the study of Donaldson's theory. Then I will review connection and curvature on Riemannian 4-manifolds, and introduce the Yang-Mills Equations. In the last part, I will discuss properties of anti-self-dual instantons and present some examples.
Lecture 2.Local Structure of Moduli Space
I will discuss the deformation complex of ASD instantons that captures the local structure of the moduli space. Then I will sketch how to achieve transversality perturbing the metrics.
Lecture 3.Compactness and Gluing of Moduli Space
I will discuss the Uhlenbeck's compactness and sketch a proof. Then I will discuss Taubes' gluing result which implies a collar structure for certain moduli spaces.
Lecture 4. Donaldson's Diagonalization Theorem
I will sketch a proof of Donaldson's diagonalization theorem that partially answers the basic questions in the first lecture.
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