Dan Freed's Home Page
Address and Phone
Department of Mathematics
University of Texas at Austin
Austin, TX 78712
(512) 471-7136 (office)
(512) 471-9038 (fax)
Email address: dafr@math.utexas.edu
Research
I have worked on a variety of problems centering around global issues in
geometry and global analysis. My work often relates to questions in
theoretical physics (quantum field theory, string theory, and condensed
matter theory), and I count physicists among my collaborators.
Some
recent papers | more
On Determinant Line Bundles
Classical Chern-Simons, Part 2 [ps, pdf]
Some Expository Papers
There are more expository papers among the links at
the recent
papers and
more
links displayed above.
1992 lectures on TQFT
2001 IAS/Park City Lectures on Field Theory and
Supersymmetry [ps, pdf]
(Unfinished) notes on Dirac operators
Lecture Notes
Notes on K-theory and string theory from a
graduate summer school "K-Theory and Quantum Fields" at the Schrodinger
Institute, June 2012.
Notes from a graduate course "Bordism: Old and
New", Fall 2013. (Comments and corrections welcome on this and all notes.)
Lecture Slides
As part of a series of lectures on the Clay problems, I spoke in April, 2001
about the Hodge conjecture. You can view the slides from the lecture [Internet Explorer, Netscape with frames/Safari, no frames]
In April, 2006 I gave the Andrejewski Lectures at the Max Planck Institute
for Mathematics in the Sciences in Leipzig. The lectures are entitled
"Twisted K-theory and the Verlinde Algebra". You can view the slides from the first lecture; the
remaining lectures were blackboard talks.
I spoke at the MSRI
25th Anniversary Celebration in January, 2008. The talk is entitled
"Remarks on Chern-Simons Theory" (slides, pdf)
Slides from a talk "The Geometry and Topology of
Orientifolds" at a workshop Topology, C*-algebras, and
String Duality, May, 2009
Slides from a talk "Dirac charge quantiation,
K-theory, and orientifolds" at a workshop "Mathematical methods in general
relativity and quantum field theories", November, 2009
Slides from a talk "Modularity and Invertibility"
at the Michael Freedman 60th Birthday Symposium, April, 2011
Slides from a talk "Remarks on fully
extended 3-dimensional topological field theories"
at String-Math, June, 2011
Slides
and paper from a talk "The Cobordism Hypothesis"
at Current Events Bulletin, Joint Mathematics Meeting, January, 2012
Slides
[pdf] from a talk "3-dimensional TQFTs
through the lens of the cobordism hypothesis"
at Stanford Topology Conference, July 2012
Slides
from a talk "4-3-2-8-7-6"
at "Aspects of Topology" in honor of Graeme Segal, Oxford, December 2012
Slides
from a talk "What is Quantum Field Theory?"
at "Berkeley Math-Physics Meeting", Berkeley, April 2015
Slides
from a talk "Unitary invertible field theories and short-range entangled
phases" at "Topological Quantum Matter", Kavli Institute for Theoretical
Physics, Santa Barbara, October 2016
Slides
from a talk "Three Applications of Topology to Physics",
Caltech, January 2018
Slides
from a talk "Two-dimensional Ising model revisited"
at "Quantum Knot Homology and Supersymmetric Gauge Theories", Aspen Center
for Physics, March 2018
Slides
from a talk "Extended topological field theory and the 2-dimensional Ising
model"
at "String-Math 2018", Sendai, Japan, June 2018
Slides
from a talk "Boundaries and 3-dimensional topological field theories"
virtually at MSRI, May 2020
Teaching
M392C: Bordism: Old and New (Fall '12)
M392C: K-theory (Fall '15)
M365C: Real Analysis (Fall '16)
M341: Linear Algebra (Fall '16)
M392C: Riemannian Geometry (Spring
'17)
M367K: Topology (Spring '18)
M392C: Index Theory (Spring '18)
M392C: Morse Theory (Fall '18)
M392C: Mathematical Gauge Theory (Spring '19)
M375T: Multivariable Analysis (Spring '19)
Outreach
Saturday Morning Math: Close Enough for
Horseshoes, Hand Grenades...and Analysis
Keynote slides (lower-res faster)
Mathematica demos from
the lecture (pdf)
Saturday Morning Math: How to Solve It
(slides)