My interest is in nonlinear geometric analysis and applications to topology, geometry, and mathematical physics. In the last years, I have been working on harmonic maps between singular spaces and applications to Teichmueller theory and three-dimensional topology.
In addition, I have been working on some nonlinear parabolic equations related to the Yang-Mills flow on Kaehler manifolds.

N/A

Research grants:

a. Principal investigator, NSF grant DMS-0204191 (2002-05), amount $187,967

b. Principal investigator, NSF grant DMS-9803606 (1998-2001), amount $83,712

24.(with R. Wentworth) Harmonic maps and Teichmueller theory, to appear in ``Handbook in Teichmueller theory'', EMS

(with R Wentworth) Convergence properties of the Yang-Mills flow on Kähler surfaces, J. Reine Angew. Math. 575 (2004), 69-99

19.(with R. Wentworth) Classification of Weil-Petersson isometries, Amer. Jour. of Math. 125 (2003), 941-975

14.(with S. Dostoglou and R. Wentworth ) Character varieties and harmonic maps to trees, Math. Reas. Lett. 5 (1998)

10.(with A.Bertram and R.Wentworth) Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians, Journ. of AMS, Vol 9, No2 (1996) 529-571.

8.(with S.Bradlow and R.Wentworth) Birational equivalences of vortex moduli, Topology, Vol 35, No 3, (1996) 731-748.

7.(with R.Wentworth) Factorization of rank 2 theta functions II, Proof of the Verlinde formula, Math. Ann. 304 (1996) 21-51.

2.(with K.Uhlenbeck) An application of transversality to the topology of stable bundles, Topology Vol 34, No 1 (1995) 203-215.

6.(with R.Wentworth) Local degeneration of the moduli space of vector bundles and factorization of rank 2 theta functions, Math. Ann. 297, (1993) 417-466.

1.The topology of the space of stable bundles over a compact Riemann surface, Journ. of Diff. Geom. 36 (1992), 699-746.

N/A

Member, Institute of Advanced Study, Princeton,
and MSRI, Berkeley

COLLABORATORS:

Chikako Mese, Johns Hopkins University;
Richard Wentworth, Johns Hopkins University;
Jonathan Weitsman, University of California, Santa Cruz.