Note:

The last lecture was delivered on Oct. 30, 2024. There is no lecture from Nov. 1 to Dec. 27, 2024.

Description：

Seiberg-Witten theory is a powerful tool in the study of low-dimensional differential topology.

This is an introduction course to the Seiberg-Witten equations (4-dimensional version) and its applications to 4-dimensional differential topology. The plan is to cover most contents in Morgan's book first (see the reference). If time permits, we may also introduce some related topics beyond Morgan's book.

Prerequisite:

Required: Smooth manifolds, connections and curvature, differential forms, basic algebraic topology (ordinary homology/cohomology), vector bundles, Sobolev spaces.

Preferred but not strictly required: Basic differential topology, characteristic classes, principle bundles, Fredholm theory and index theory of elliptic operators.

Main reference:

The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44) by John W. Morgan

Registration: https://www.wjx.top/vm/hwt72X7.aspx#