Preprints and Publications
  1. Higgs bundles, isomonodromic leaves and minimal surfaces. (with Brian Collier and Jérémy Toulisse). 59 pp. pdf
  2. Z/2 harmonic 1-forms, R-trees, and the Morgan-Shalen compactification (with Siqi He and Boyu Zhang). 36 pp. pdf
  3. Conformal limits for parabolic SL(n,C)-Higgs bundles (with Brian Collier and Laura Fredrickson). 50 pp. pdf
  4. Wild orbits and generalised singularity modules: stratifications and quantisation (with Damien Calaque, Giovanni Felder, and Gabriele Rembado). 112 pp. pdf
  5. Complex Chern-Simons bundles in the relative setting (with Dennis Eriksson and Gerard Freixas i Montplet). 132 pp. To appear in Astérisque. pdf
  6. The algebraic and analytic compactifications of the Hitchin moduli space (with Siqi He, Rafe Mazzeo, and Xuesen Na). Moduli 1 (2024), 45 pp. pdf
  7. Geometrization of the TUY/WZW/KZ connection (with Indranil Biswas and Swarnava Mukhopadhyay). Lett. Math. Phys. 114 (2024), no. 3, Paper No. 85, 39 pp. pdf
  8. The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type (with Xuemiao Chen). Math. Res. Lett. 31 (2024), no. 3, 639–654. pdf
  9. A parabolic analog of a theorem of Beilinson and Schechtman (with Indranil Biswas and Swarnava Mukhopadhyay). Int. Math. Res. Not. IMRN(2024), no. 13, 10319–10348. pdf
  10. Higgs bundles, harmonic maps, and pleated surfaces (with Andreas Ott, Jan Swoboda, and Michael Wolf). Geom. Topol. 28:7 (2024) 3135–3220. pdf
  11. A Meyer-Vietoris formula for the determinant of the Dirichlet-to-Neumann operator on Riemann surfaces. J. Geom. Anal. 33 (2023), no. 2, 1-27. pdf
  12. A Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles on degenerating families (with Xuemiao Chen). Math. Annalen 388, no. 2 (2023), 1903-1935. pdf
  13. Compactness for Ω-Yang-Mills connections. (with Xuemiao Chen). Calc. Var. Partial Differential Equations 61 (2022), no. 2, Paper No. 58, 30 pp. pdf
  14. A Hitchin connection on nonabelian theta functions for parabolic G-bundles. (with Indranil Biswas and Swarnava Mukhopadhyay). J. Reine Angew. Math. 803 (2023), 137-181. pdf
  15. Continuity of the Yang-Mills flow on the set of semistable bundles (with Benjamin Sibley). Pure Appl. Math. Q. 17 (2021), No. 3, pp. 909-931. pdf
  16. Complex algebraic compactifications of the moduli space of Hermitian-Yang-Mills connections on a projective manifold (with Daniel Greb, Benjamin Sibley, and Matei Toma). Geom. Topol. 25 (2021), no. 4, 1719–-1818. pdf
  17. Spectral data for spin Higgs bundles (with Swarnava Mukhopadhyay). Int. Math. Res. Not. IMRN 2021, No. 6, pp. 4211-4230. pdf
  18. Deligne pairings and families of rank one local systems on algebraic curves (with Gerard Freixas i Montplet). J. Diff. Geom. 115 (2020), no. 3, 475-528. pdf
  19. Conformal limits and the Bialynicki-Birula stratification of the space of λ-connections. (with Brian Collier). Adv. Math. 350 (2019) 1193-1225. pdf
  20. Generalized theta functions, strange duality, and odd orthogonal bundles on curves (with Swarnava Mukhopadhyay). Commun. Math. Phys. 370 (2019), no. 1, 325-376. pdf
  21. Flat line bundles and the Cappell-Miller torsion in Arakelov geometry (with Gerard Freixas i Montplet). Ann. Sci. Ec. Norm. Super. 52 (2019), no. 5, 1265-1303. pdf
  22. Variations along the Fuchsian locus (with François Labourie). Ann. Sci. Ec. Norm. Super. 51 (2018), no. 2, 487-547. pdf
  23. Higgs bundles and local systems on Riemann surfaces. "Geometry and quantization of moduli spaces," 165-219. CRM Advanced Courses in Mathematics. Birkhauser/Springer, 2016. pdf
  24. Surface group representations to SL(2,C) and Higgs bundles with smooth spectral data (with Michael Wolf). Geom. Topol. 20 (2016), no. 5, 3019-3032. pdf
  25. A symplectic analogue of the Quot scheme (with Indranil Biswas, Ajneet Dhillon, and Jacques Hurtubise). C. R. Acad. Sci. Paris, Ser. I 353 (2015) 995-999. pdf
  26. A generalized Quot scheme and meromorphic vortices (with Indranil Biswas, Ajneet Dhillon, and Jacques Hurtubise). Adv. Theor. Math. Phys. 19 (4) (2015), 905-921. pdf
  27. Analytic cycles, Bott-Chern forms, and singular sets for the Yang-Mills flow on Kaehler manifolds (with Benjamin Sibley). Adv. Math. 279 (2015), 501-531. abs pdf
  28. Cohomology of U(2,1) representation varieties of surface groups (with G. Wilkin). Proc. London Math. Soc. (3) 106 (2013), 445-476. abs pdf
  29. Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces . Commun. Analysis Geom. 20 (3) (2012), 455--500. abs pdf addendum
  30. Morse theory and stable pairs (with G. Wilkin). In "Variational Problems in Differential Geometry," R. Bielawski, K. Houston, and M. Speight, eds., London Mathematical Society Lecture Note Series No. 394, Cambridge University Press, 2012, 142--181. abs pdf
  31. Morse theory and hyperkaehler Kirwan surjectivity for Higgs bundles (with G. Daskalopoulos, J. Weitsman, and G. Wilkin). J. Diff. Geom. 87 (1) (2011), 81--116. abs pdf
  32. Cohomology of SL(2,C) character varieties of surface groups and the action of the Torelli group (with G. Daskalopoulos and G. Wilkin). Asian J. Math. 14 (3) (2010), 359--384. abs pdf
  33. The action of the mapping class group on representation varieties. In "Transformation Groups and Moduli Spaces of Curves," L. Ji and S.-T. Yau, eds., Advanced Lectures in Mathematics 16, Higher Education Press and International Press, 2011, 277-299. abs pdf
  34. On products of isometries of hyperbolic space (with E. Falbel). Top. Appl. 156 (13) (2009), 2257--2263. abs pdf
  35. Precise constants in bosonization formulas on Riemann surfaces I. Commun. Math. Phys. 282 (2) (2008), 339--355. abs pdf
  36. Energy of harmonic maps and Gardiner's formula. In the tradition of Ahlfors-Bers. IV, 221--229, Contemp. Math., 432, Amer. Math. Soc., Providence, RI, 2007. abs pdf
  37. Harmonic maps and Teichmueller theory (with G. Daskalopoulos). Handbook of Teichmueller theory. Vol. I, 33--109, IRMA Lect. Math. Theor. Phys., 11, Eur. Math. Soc., Z¸rich, 2007. abs pdf
  38. On the blow-up set of the Yang-Mills flow on Kaehler surfaces (with G. Daskalopoulos). Math. Z. 256 (2007), 301-310. abs pdf
  39. Energy of twisted harmonic maps of Riemann surfaces (with W. Goldman). In the tradition of Ahlfors-Bers. IV, 45--61, Contemp. Math., 432, Amer. Math. Soc., Providence, RI, 2007. abs pdf
  40. Holomorphic frames for weakly converging holomorphic vector bundles (with G. Daskalopoulos). Can. Math. Bull. 49 (1) (2006), 36-40. abs pdf
  41. Eigenvalues of products of unitary matrices and Lagrangian involutions (with E. Falbel). Topology 45 (2006), 65-99. abs pdf
  42. Convergence properties of the Yang-Mills flow on Kaehler surfaces (with G. Daskalopoulos). J. reine angew. Math. 575 (2004), 69-99. abs pdf erratum
  43. Classification of Weil-Petersson isometries (with G. Daskalopoulos). Amer. J. Math. 125 (2003), 941-975. abs pdf
  44. Harmonic maps to Teichmueller space (with G. Daskalopoulos and L. Katzarkov). Math. Res. Lett. 7 (2000), 133-146. abs pdf
  45. On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups (with G. Daskalopoulos and S. Dostoglou). Duke Math. J. 101 (2000), 189-207. abs pdf
  46. The Yang-Mills flow near the boundary of Teichmueller space (with G. Daskalopoulos). Math. Annalen 318 (1) (2000), 1-42. abs pdf
  47. On the Brill-Noether problem for vector bundles (with G. Daskalopoulos). Forum Math. 11 (1) (1999), 63-77. abs pdf
  48. Character varieties and harmonic maps to R-trees (with G. Daskalopoulos and S. Dostoglou). Math. Res. Lett. 5 (4) (1998), 523-534. abs pdf
  49. Families of SU(2) representations for mapping cylinders of periodic monodromy (with G. Daskalopoulos and S. Dostoglou). Proc. Edinburgh Math. Soc. 40 (1997), 383-392. pdf
  50. Mumford-Thaddeus principle on the moduli space of vector bundles on an algebraic surface (with K. Matsuki). Int. J. Math. 8 (1997), 97-148. abs pdf
  51. Geometric quantization for the moduli space of vector bundles with parabolic structure (with G. Daskalopoulos). In "Geometry, Topology and Physics," Proceedings of the First Brazil-USA Workshop, Campinas, Brazil, June 30- July 7, 1996. B.N. Apanasov, S.B. Bradlow, W.A. Rodrigues, Jr., K.K. Uhlenbeck (Editors), Walter de Gruyter Publishers, 119-155. abs pdf
  52. The multi-monopole equations for Kaehler surfaces (with J. Bryan). Turk. J. Math. 20 (1996), 119-128.
  53. Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians (with A. Bertram and G. Daskalopoulos). J. Amer. Math. Soc. 9 (1996), 529-571. abs pdf
  54. Birational equivalence of vortex moduli (with S. Bradlow and G. Daskalopoulos). Topology 35 (1996), 731-748. abs pdf
  55. Factorization of rank two theta functions II: Proof of the Verlinde formula (with G. Daskalopoulos). Math. Annalen 304 (1996), 21-51. abs pdf
  56. Moduli of extensions of holomorphic vector bundles on Kaehler manifolds (with G. Daskalopoulos and K. Uhlenbeck). Commun. Analysis Geom. 3 (1995), 479-522. pdf
  57. Stable augmented bundles over Riemann surfaces (with S. Bradlow, G. Daskalopoulos, and O. Garcia-Prada). In Vector Bundles in Algebraic Geometry, London Mathematical Society Lecture Notes, Cambridge University Press, 1995, 15-67.
  58. Local degeneration of the moduli space of vector bundles and factorization of rank two theta functions I (with G. Daskalopoulos). Math. Annalen 297 (1993), 417-466. abs pdf
  59. The integrability criterion in Chern-Simons gauge theory (with G. Daskalopoulos). Commun. Math. Phys. 151 (1993), 437-445. pdf
  60. Spectral convergence on degenerating surfaces (with L. Ji). Duke Math. J. 66 (1992), 469-501. abs pdf erratum
  61. Asymptotics of determinants from functional integration. J. Math. Phys. 32 (7) (1991), 1767-1773. abs pdf erratum
  62. The asymptotics of the Arakelov-Green’s function and Faltings’ delta invariant. Commun. Math. Phys. 137 (1991), 427-459. abs pdf