Editing Lecture Schedule

====== Lectures =======

Tentative lecture plan is as follows: 

=== Week 1 ===
Topics: Review of differential geometry
  * Topological and smooth manifolds,
  * Vector and tensor fields,
  * Algebra of differential forms,
  * De Rham Cohomology

Reading: 
  * Taubes Ch 1
  * Frenkel Sections 1-3
  * Nakahara Sections 5.1, 5.2, 5.4. 6.
  * Sontz Chapters 2, 3, 5 

=== Week 2 ===
Topics: Review of differential geometry
  * vector fields
  * Lie brackets
  * diffeomorphisms
  * Lie derivatives
  * Lie groups and Lie algebras.
  * Exponential maps
  * adjoint representation
  * Basics of Symplectic Geometry
  * Hamiltonian vector fields
  * Hamiltonian group actions
  * Moment maps and co-moment maps.

Reading:
  * Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:
  * Further details on smooth actions,
  * Symplectic structure on cotangent bundles
  * Quotients of free, proper, smooth actions
  * Principal bundles.
  * Frame bundles.
  * Associated fibre bundles.


Reading: 

=== Week 4 ===
Topics: 
  * Associated fibre bundles: vector bundles, adjoint bundle.
  * Reduction and extension of structure group. 
  * Group of gauge transformations. 
  * Linear connections.

Reading: 

=== Week 5 ====
Topics: 
  * Connections: Koszul connections, principal connections, Ehresmann connections. 
  * Equivalences between them. 
  * Atiyah sequence and differential operators.

Reading: