John Baez's Stuff
This Week's Finds
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
Here are notes from some more elementary classes:
- 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
- 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
- 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
- Spring 2005 -
conclusion of the course on gauge theory and
- Fall 2006 - the seminar
this quarter covers two subjects:
and cohomology, and
quantum computation. Now with blog entries where you can
- Winter 2007 - continuation
of the courses on
and cohomology and
- Spring 2007 - continuation
of the courses on
and cohomology and
- Fall 2007 - beginning of
of a seminar on geometric representation theory, taught by
John Baez and James Dolan. With videos of the lectures.
- Winter 2008 - continuation of
the seminar on geometric representation theory. With videos.
- Fall 2008 - a course on
Lie theory through examples.
- Fall 2015 - how category theory
makes it easier to learn lots of mathematics.
- Winter 2016 - an introductory course on
- Fall 2016 - an introduction to linear
- Fall 2018 - how category theory helps
us to understand the essence of mathematics.
- Fall 2019 - combinatorics through
species and their generating functions.
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
© 2005 John Baez