Introduction to 4-dimensional Seiberg-Witten theory

Speaker：Weifeng Sun 孙巍峰

Weifeng Sun is an Assistant Professor at YMSC. He holds a Ph.D. in Mathematics from Harvard University (2021) and a B.S. in Mathematics from Tsinghua University (2016). He has been the Szego Assistant Professor at Stanford University since 2021, with an expected tenure until 2024. His research areas encompass gauge theory, low dimensional geometry and topology. Recently, his research mainly focuses on the Bogomolny equations and theextended Bogomolny equations.

Time：

Wed. & Fri., 13:30-15:05,

Oct. 9-Dec. 27, 2024

Venue：

C654, Shuangqing Complex Building A

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