Here are notes from my seminar. It was originally called
the Quantum Gravity Seminar, but it's always
covered a wide range of topics in mathematical physics.
There's a huge amount of stuff here! — including notes
from more elementary classes that I've
taught. If you're interested in LaTeXing any
of these notes, let me know. We've already done this with some of the
'00-'01
and
'06-'07 notes.
Fall 2000 -
introduction to spin networks and the Lagrangian approach to
gauge theories and gravity. Includes another appearance
of Oz and the Wizard!
Winter 2001 -
continuation of the Fall 2000 session, covering topological
quantum field theories and quantum electromagnetism in 2d spacetime.
Also, still more tales featuring Oz and the Wizard!
Spring 2001 -
continuation of the Winter 2001 session,
covering the representation theory of quantum SU(2) and its
application to a 3d topological quantum field theory called
the Turaev-Viro model.
Fall 2001 - continuation of
the Spring 2001 session, covering the basics of loop quantum gravity.
Winter 2002 - beginning of a
course on categorified gauge theory. An introduction to
n-categories, with a special emphasis on 2-groups and their
application to categorified electromagnetism, also known as
2-form electromagnetism.
Spring 2002 - continuation
of the course on categorified gauge theory. Groups and 2-groups,
bundles and 2-bundles!
Fall 2002 -
introduction to diagrammatic methods in
group representation theory, leading up to the theory of
Feynman diagrams.
Winter 2003 - no seminar: I was on sabbatical.
Spring 2003 - a course on
Clifford algebras, spinors, the Dirac equation, and algebraic
patterns in the Standard Model of particle physics, leading up
to the SU(5) grand unified theory.
Fall 2003 -
beginning of a course on quantization
and categorification, which explains how Feynman diagrams and
a wealth of other combinatorics fall out as a natural consequence
of categorifying the harmonic oscillator.
Winter 2004 -
continuation of the course on quantization
and categorification. Lots of fun combinatorics: counting
things with generating functions!
Spring 2004 -
conclusion of the course on quantization
and categorification. Stuff types, stuff operators
and categorified Feynman diagrams.
Fall 2004 -
beginning of a course on gauge theory and
topology, starting with a history of n-categorical
physics and moving on to the construction of 2d
topological quantum field theories.
Winter 2005 -
continuation of the course on gauge theory and
topology. 3d topological quantum
field theories, Dijkgraaf-Witten models and group
cohomology!
Spring 2005 -
conclusion of the course on gauge theory and
topology.
The mathematician does not dig for lost artifacts of a
vanished civilization but for the fundamental patterns that
undergird the universe, and like the archaeologist we usually
find only small fragments. - David M. Bressoud