Introduction to Moduli spaces (2016 Spring)




Course Description

We would like to introduce varies moduli spaces this semester. The material that we would like to cover in the course includes the following:

References («ÝÄò)

Background: Motivation: Yang-Mills: Principal connections and Holonomy: Vector bundles and their moduli: Complex geometry: Related papers:

Syllabus

  • 2/16: Lie groups, fiber bundles, principal bundles, associated bundles
  • 2/23: gauge transformations, connections
  • 3/1: Move to 6/14
  • 3/8: curvature 2-form, gauge action
  • 3/15: Yang-Mills functional
  • 3/22: moduli space of flat bundles
  • 3/29: connections on a vector bundle
  • 4/5: National Holiday

  • 4/12: almost complex structure
  • 4/19: holomorphic structure on a complex vector bundle
  • 4/26: Harder-Narasimhan filtration, Narasimhan-Seshadri Theorem
  • 5/3: Move to 6/14
  • 5/10: Hermitian connections
  • 5/17: Relation between the three moduli spaces
  • 5/24: Hitchin equations and various moduli spaces
  • 5/31: Kahler and hyperKahler quotients
  • 6/7: Morse theory as an application on the moduli space's topology Starts at 12
  • 6/14: Final presentations Starts at 11 am at room 734

Evaluation


Last Updated: June 8, 2016
URL: http://www.math.nthu.edu.tw/~nankuo/IMS.html