Button to scroll to the top of the page.

Daniel S Freed

Department of Mathematics

Mildred Caldwell and Baine Perkins Kerr Centennial Professorship in Mathematics (Holder)

Differential Geometry


Phone: 512-471-7136

Office Location
PMA 9.162

Postal Address
AUSTIN, TX 78712

Ph.D., University of California, Berkeley (1985)

Research Interests

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 M-theory), and I count physicists among my collaborators.


1. (with K. Uhlenbeck), Instantons and Four-Manifolds", MSRI Publications, Volume 1, SpringerVerlag, New York, 1984, 1991 (Second Edition).

2. "Five Lectures on Supersymmetry", American Mathematical Society, Providence, RI, 1999.

Books Edited

3. (edited with K. Uhlenbeck), Geometry and Quantum Field Theory", IAS/Park City Mathematics Series, 1. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1995.

4. (edited with P. Deligne, P. Etingof, L. Jeffrey, D. Kazhdan, J. Morgan, D. Morrison, E. Witten), Quantum Fields and Strings: A Course for Mathematicians", American Mathematical Society, Providence, RI, 1999.

5. (edited with D. Morrison, I. Singer), Quantum Field Theory, Supersymmetry, and Enumerative Geometry", IAS/Park City Mathematics Series, 11. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2006.

Research Articles

6. (with L. A. Shepp), A poisson process whose rate is a hidden Markov process, Advances in Applied Probability, 14 (1982), 21{36.

7. (with Jean-Michel Bismut) Fibre determinant et invariant ^eta, C. R. Acad. Sci. Paris. Ser. I
Math., 301 (1985), 707{710.

8. Flag manifolds and Kahler geometry, In nite Dimensional Groups (ed. V.G. Kac), MSRI Publications, Volume 4, Springer-Verlag, New York, 1985.

9. (with P. C. Fishburn, P. Frankl, J. C. Lagarias, A. M. Odlyzko), Probabilities for intersecting
systems and random subsets of nite sets, SIAM J. Alg. Disc. Meth., 7 (1986), 73{79.

10. (with Jean-Michel Bismut), The analysis of elliptic families. I. Metrics and connections on determinant bundles, Commun. Math. Phys., 106 (1986), 159{176.

11. (with Jean-Michel Bismut), The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem, Commun. Math. Phys., 107 (1986), 103{163.

12. Determinants, Torsion, and Strings, Commun. Math. Phys., 107 (1986), 483{513.

13. (with Cumrun Vafa), Global anomalies on orbifolds, Commun. Math. Phys., 110 (1987), 349{389.

14. On determinant line bundles, in Mathematical Aspects of String Theory" (ed. S. T. Yau), World Scienti c Publishing, 1987.

15. Z=k-Manifolds and families of Dirac operators, Invent. Math., 92 (1988), 243{254.

16. The geometry of loop groups, J. Diff. Geom., 28 (1988), 223{276.

17. An index theorem for families of Fredholm operators parametrized by a group, Topology, 27 (1988), 279{300.

18. (with David Groisser), The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group, Mich. Math J., 36 (1989), 323{344.

19. Anomalies and determinant line bundles, XVIIth International Colloquium on Group Theoretical Methods in Physics (Sainte-Adele, PQ, 1988), World Scienti c Publishing, Teaneck, NJ,1989.

  • 2012 Fellow of the American Mathematical Society
  • 2005-2007 Cook Professorship in Mathematics
  • 2002-2003 Guggenheim Fellow
  • 2002 College of Natural Sciences Outreach Award
  • 1990-1996 NSF Presidential Young Investigator Award
  • 1988-1992 Alfred P. Sloan Research Fellowship
  • 1985-1988 NSF Postdoctoral Fellowship in Mathematics
  • 1981-1984 NSF Graduate Fellowship