Updated outline

This post has been migrated from my old blog, the math-physics learning seminar.

I was thinking about how to put this blog to use, and especially how to make it worthwhile for myself. In 2010, I ran a learning seminar on math/physics which in my opinion was extremely successful. I made detailed notes for nearly all of the talks, and I had several people ask me at the end of the seminar to give them copies of the notes I had made. We managed to do something very special in the seminar, and I think it’s worth writing up notes from the best talks (and reorganizing/elaborating/etc. when necessary) and putting them online for all to see. It gives me a chance to practice my math writing, and if I ever run another seminar of this flavor (or teach a course, or write a book…) then a lot of the work will already be done for me.

Here is a rough outline of the topics we covered (or that need to be covered as background):

• Classical mechanics and symplectic geometry

  • Hyperkähler reduction
  • Legendre transform
  • Classical mechanics, part 1
  • Classical mechanics, part 2
  • Classical mechanics, part 3
  • Classical mechanics, part 4
  • Classical mechanics, part 5
  • Classical mechanics, part 6
  • Classical partition function
  • Noether’s theorem
  • Generating functions for symplectomorphisms

• Completely integrable systems.

  • KAM theory

• Special relativity.

• Classical field theory.

• Classical electrodynamics.

• General relativity

  • Geometry of spacetime, part 1
  • Geometry of spacetime, part 2
  • Geometry of spacetime, part 3
  • Geometry of spacetime, part 4
  • Geometry of spacetime, part 5

• Quantization (canonical, deformation, geometric, etc.)

  • Lattice quantum mechanics
  • Quantum Hamiltonian reduction
  • Moyal product
  • Weyl-Wigner transform

• Path integrals in quantum mechanics.

  • Path integrals, part 1
  • Path integrals, part 2
  • Path integrals, part 3

• Perturbation theory and Feynman diagrams.

  • Introduction to Gaussian integrals
  • Gaussian integrals and Wick’s theorem

• Feynman rules for QED.

• Berezin integration and quantization of fermionic fields.

• Gauge fields.

• Clifford algebras and spin

  • Clifford algebras, part 1
  • Clifford algebras, part 2
  • Clifford algebras, part 3

• BRST quantization and related topics

  • BRST
  • BRST Lie algebra
  • Fadeev-Popov ghosts
  • Fadeev-Popov ghosts, continued
  • Quantum BV complex

• Path integral proof of the index theorem

• Additional topics in quantum field theory

  • Spontaneous symmetry breaking
  • Lectures on Seiberg-Witten theory
  • BPS and wall-crossing
  • Seiberg-Witten theory and Riemann-Hilbert correspondance
  • 1PI effective action

• Virasoro algebra and CFT

  • Circle diffeomorphisms
  • Virasoro algebra
  • Virasoro algebra for a free boson

As you can see, it was an ambitious seminar! I will update the outline as I go through my old notes and start posting them.