Dan Freed's Home Page

Shiing-Shen Chern Professor of Mathematics, Harvard University
Director of the Center of Mathematical Sciences and Applications (CMSA)

Curriculum vita [pdf]

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


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 "Quantum theory from a geometric viewpoint, Part I", Fall 2023.

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

Slides from a talk "Complex Chern-Simons invariants of 3-manifolds via abelianization", Geometry Conference: 50 years of Nigel Hitchin's Mathematics, December 2023


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)


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)