George Daskalopoulos

Professor of Mathematics

Email: daskal<at>math.brown.edu

 

Mailing Address:
Mathematics Department
Box 1917
Brown University
Providence, RI 02912

 

RESEARCH INTERESTS - Differential Geometry, Gauge Theory, Geometric Analysis

BACKGROUND - Education: Ph.D., Chicago, 1989

RECENT PUBLICATIONS

  • Daskalopoulos, Georgios; Mese, Chikako; Wilkin, Graeme; Higgs bundles over cell complexes and representations of finitely presented groups. Preprint.
  • Daskalopoulos, Georgios; Mese, Chikako; On the singular set of a nonlinear degenerate PDE arising in Teichmueller theory. Preprint.
  • Daskalopoulos, Georgios; Mese, Chikako; Rigidity of Teichmueller space. Preprint.
  • Daskalopoulos, Georgios; Mese, Chikako; Sanders Adrew; Vdovina Alina; Surface groups acting on CAT(-1) spaces. To appear in Ergodic Theory and Dynamical Systems.
  • Daskalopoulos, Georgios; Mese, Chikako; Essential Regularity of the Model Space for the Weil-Petersson Metric. To appear in Journal für die reine und angewandte Mathematik (Crelles Journal).
  • Daskalopoulos, Georgios; Mese, Chikako; C1-Estimates for the Weil-Petersson Metric. Transactions of the AMS 369 (2017), 2917-2950.
  • Daskalopoulos, Georgios; Mese, Chikako; On the Singular Set of Harmonic Maps into DM-Complexes. Memoirs of the American Math.Soc. Vol 239, no 1129, (2016).
  • Daskalopoulos, Georgios; Mese, Chikako; Monotonicity Properties of Harmonic maps into NPC spaces. J. Fixed Point Theory Appl. 11 (2012) 225–243.
  • Daskalopoulos, Georgios; Mese, Chikako; Vdovina Alina; Superrigidity of Hyperbolic Buildings. GAFA Vol. 21 (2011) 905–919.
  • Daskalopoulos, Georgios; Weitsman Jonathan; Wentworth, Richard; Wilkin Graeme; Morse theory and hyperkaehler Kirwan surjectivity for Higgs bundles. J. Diff. Geom. 87 (2011) 81-115.
  • Daskalopoulos, Georgios; Wentworth, Richard; Wilkin Graeme; Cohomology of SL(2, C) Character varieties of surface groups and the action of the Torelli group. Asian Jour. of Math. Vol 14, no3, pp.359-384, (2010).
  • Daskalopoulos, Georgios; Mese, Chikako Harmonic Maps between singular spaces I. Communications in Analysis and Geometry Volume 18, Number 2 (2010), 257–337. 
  • Daskalopoulos, Georgios; Mese, Chikako Fixed point and rigidity theorems for harmonic maps from simplicial complexes into NPC spaces. Geom Dedica (2009) 141:33–57.
  • Daskalopoulos, Georgios; Mese, Chikako Harmonic maps from a simplicial complex and geometric rigidity. J. Diff. Geom. 78 (2008) 269-293.
  • Daskalopoulos, Georgios; Mese, Chikako Harmonic maps from 2-complexes.Comm. Anal. Geom. 14 (2006), no. 3, 497--549. 
  • Daskalopoulos, Georgios; Wentworth, Richard Holomorphic frames for weakly converging holomorphic vector bundles. Canad. Math. Bull. 49 (2006), no. 1, 36--40. 
  • Daskalopoulos, Georgios; Wentworth, Richard Convergence properties of the Yang-Mills flow on Kähler surfaces. J. Reine Angew. Math. 575 (2004), 69--99. 
  • Daskalopoulos, Georgios; Wentworth, Richard Classification of Weil-Petersson isometries. Amer. J. Math. 125 (2003), no. 4, 941--975. 
  • Daskalopoulos, Georgios; Wentworth, Richard The Yang-Mills flow near the boundary of Teichmüller space. Math. Ann. 318 (2000), no. 1, 1--42. 
  • Daskalopoulos, Georgios; Katzarkov, Ludmil; Wentworth, Richard Harmonic maps to Teichmüller space. Math. Res. Lett. 7 (2000), no. 1, 133--146. 
  •  
  • Daskalopoulos, G.; Dostoglou, S.; Wentworth, R. On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups. Duke Math. J. 101 (2000), no. 2, 189--207. 
  •  
  • Daskalopoulos, Georgios; Wentworth, Richard On the Brill-Noether problem for vector bundles. Forum Math. 11 (1999), no. 1, 63--77. 
  •  
  • Daskalopoulos, G.; Dostoglou, S.; Wentworth, R. Character varieties and harmonic maps to R-trees. Math. Res. Lett. 5 (1998), no. 4, 523--53.
  •  
  • Daskalopoulos, Georgios; Wentworth, Richard Geometric quantization for the moduli space of vector bundles with parabolic structure. Geometry, topology and physics (Campinas, 1996), 119--155, de Gruyter, Berlin, 1997. 
  • Daskalopoulos, G.; Dostoglou, S.; Wentworth, R. Families of SU(2) representations for mapping cylinders of periodic monodromy. Proc. Edinburgh Math. Soc. (2) 40 (1997), no. 2, 383--392.
  • Bradlow, Steven; Daskalopoulos, Georgios; Wentworth, Richard Birational equivalences of vortex moduli. Topology 35 (1996), no. 3, 731--748. 
  • Daskalopoulos, Georgios; Wentworth, Richard Factorization of rank two theta functions. II. Proof of the Verlinde formula. Math. Ann. 304 (1996), no. 1, 21--51. 
  • Bertram, Aaron; Daskalopoulos, Georgios; Wentworth, Richard Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians. J. Amer. Math. Soc. 9 (1996), no. 2, 529--571. 
  • Daskalopoulos, Georgios; Uhlenbeck, Karen; Wentworth, Richard Moduli of extensions of holomorphic bundles on Kähler manifolds. Comm. Anal. Geom. 3 (1995), no. 3-4, 479--522.
  • Bradlow, Steven; Daskalopoulos, Georgios; García-Prada, Oscar; Wentworth, Richard Stable augmented bundles over Riemann surfaces. Vector bundles in algebraic geometry (Durham, 1993), 15--67, London Math. Soc. Lecture Note Ser., 208, Cambridge Univ. Press, Cambridge, 1995. 
  • Daskalopoulos, Georgios; Uhlenbeck, Karen An application of transversality to the topology of the moduli space of stable bundles. Topology 34 (1995), no. 1, 203--215.
  • Bradlow, Steven; Daskalopoulos, Georgios Moduli of stable pairs for holomorphic bundles over Riemann surfaces. II. Internat. J. Math. 4 (1993), no. 6, 903--925.
  • Daskalopoulos, Georgios; Wentworth, Richard Local degeneration of the moduli space of vector bundles and factorization of rank two theta functions. I.Math. Ann. 297 (1993), no. 3, 417--466.
  • Daskalopoulos, Georgios; Wentworth, Richard The integrability criterion in SU(2) Chern-Simons gauge theory. Comm. Math. Phys. 151 (1993), no. 3, 437--445. 
  • Daskalopoulos, Georgios The topology of the space of stable bundles on a compact Riemann surface. J. Differential Geom. 36 (1992), no. 3, 699--746. 
  • Bradlow, Steven; Daskalopoulos, Georgios Moduli of stable pairs for holomorphic bundles over Riemann surfaces. Internat. J. Math. 2 (1991), no. 5, 477--513.