Instructor: Shuguang Wang

Description: The purpose is to use Seiberg-Witten equations as a modern example to illustrate applications of some of the fundamental tools from Geometry and Topology, such as Clifford algebra, Dirac operators, Fredholm theory, Banach manifolds, K-theory, characteristic classes, Index Theorem, Sard-Smale theorem, etc. These tools have found other wide applications in various mathematical areas. Students of the class will be guided to pursue independent studies of those topics listed above, which suit their individual interests.

Main Textbook: The Seiberg-Witten equations and applications to the topology of smooth 4-manifolds, by John Morgan, Princeton Mathematical Notes V44, 1996.

Prerequisite: Basic knowledge in Differential Geometry, Differential Topology, and Algebraic Topology. Any student with knowledge about the following concepts is encouraged to sign in the class: differential manifolds, complex manifolds, vector bundles, connections, differential operators, (co)homology groups.