Dan Freed's Home Page
Contact Information
Harvard University
Department of Mathematics
Science Center Room 325
1 Oxford Street
Cambridge, MA 02138
(617) 495-2171
Email address: dafr@math.harvard.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.
Papers
on arXiv
On Determinant Line Bundles
Classical Chern-Simons, Part 2 [ps, pdf]
Some Expository Books and Lecture Notes
There are also expository papers at
the arXiv
link displayed above.
2022 Perimeter Institute Lectures on Finite
Symmetry in QFT
2017 CBMS Lectures on Field Theory and Topology
2012 Lectures on Twisted K-Theory and Orientifolds
2001 IAS/Park City Lectures on Field Theory and
Supersymmetry
1992 lectures on TQFT
(Unfinished) Notes on Dirac Operators
Course Notes
These lecture notes are rough in places, so please use with caution!
Comments, corrections, and suggestions welcome; please email me.
Notes from a graduate course "Differential
Topology", Spring 2021 and Spring 2022.
Notes from an advanced undergraduate course
"Multivariable Analysis", Spring 2019. The notes cover differential calculus
in several (and infinitely many) variables, differential forms in affine
space, fundamental theorem of ODE, and a bit of calculus of variations and
the geometry of curves and surfaces.
Notes from a graduate course "Bordism: Old and
New", Fall 2013.
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
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
Slides from a talk "The Atiyah-Singer index theorem"
virtually at CMSA Memorial Conference for the founders of index theory:
Atiyah, Bott, Hirzebruch and Singer, April 2021
Slides from a talk "A time-reversal anomaly,
bordism, and index theory"
Segal 80th Birthday Conference "Physics from the Point of View of Geometry", September 2022
Slides from a talk "Topological symmetry in field theory",
CMSA, November 2022
Slides from a talk "What are topological symmetries in QFT",
Simons Foundation, November 2022
Slides from a talk "What is an anomaly?",
Mathematical Picture Language Seminar, February 2023
Teaching
M392C: Bordism: Old and New (Fall
'12) -- see above for notes
M392C: K-theory (Fall '15)
M392C: Riemannian Geometry (Spring
'17)
M392C: Index Theory (Spring '18)
M392C: Morse Theory (Fall '18)
M392C: Mathematical Gauge Theory (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)