
Daniel S Freed
Professor
Department of Mathematics
Mildred Caldwell and Baine Perkins Kerr Centennial Professorship in Mathematics  Frank E. Gerth III Faculty FellowshipsDifferential Geometrydafr@math.utexas.edu
Phone: 5124717136
Office Location
RLM 9.162
Postal Address
2515 SPEEDWAY
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 Mtheory), and I count physicists among my collaborators.

Books
1. (with K. Uhlenbeck), Instantons and FourManifolds", 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 JeanMichel Bismut) Fibre determinant et invariant ^eta, C. R. Acad. Sci. Paris. Ser. I
Math., 301 (1985), 707{710.8. Flag manifolds and Kahler geometry, Innite Dimensional Groups (ed. V.G. Kac), MSRI Publications, Volume 4, SpringerVerlag, 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 JeanMichel Bismut), The analysis of elliptic families. I. Metrics and connections on determinant bundles, Commun. Math. Phys., 106 (1986), 159{176.
11. (with JeanMichel 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 Scientic Publishing, 1987.
15. Z=kManifolds 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 (SainteAdele, PQ, 1988), World Scientic Publishing, Teaneck, NJ,1989.

 2012 Fellow of the American Mathematical Society
 20052007 Cook Professorship in Mathematics
 20022003 Guggenheim Fellow
 2002 College of Natural Sciences Outreach Award
 19901996 NSF Presidential Young Investigator Award
 19881992 Alfred P. Sloan Research Fellowship
 19851988 NSF Postdoctoral Fellowship in Mathematics
 19811984 NSF Graduate Fellowship