Dan Freed's Home Page

I am a professor in the Department of Mathematics at the University of Texas at Austin. For more information about the Geometry Group here in Austin, please follow the indicated link.

Curriculum vita [pdf]

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


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


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)


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)