• On the first Betti number of a hyperbolic manifold, Annals of Mathematics,  104 (1976)
    • A postscript version of this article is available here.

  • Closed geodesics and the eta invariant, Annals of Mathematics, 108 (1978).
    • A postscript version of this article is available here.
     
     

    CONTROLLING DIFFERENTIAL GRADED LIE ALGEBRAS

  • P. Deligne's 1986 Letter on Controlling Differential Graded Lie Algebras
    • To obtain a copy of this letter in pdf format click here .
     
  • The Deformation Theory of Representations of Fundamental Groups of Compact Kahler
    Manifolds (with W. Goldman), Publ. Math. I.H.E.S.; 67(1988)
    • To obtain a copy of this paper in pdf format click here .
     
     

    THE THETA CORRESPONDENCE AND INTERSECTION NUMBERS OF CYCLES

  • Intersection Theory of Cycles on Locally Symmetric Spaces and Fourier Coefficients
    of Holomorphic Modular Forms in Several Complex Variables (with S. Kudla), Publ. Math. I.H.E.S.; 71(1990)

    • To obtain a copy of this paper in pdf format click here .
     
     

    FROM THE NOT-SO-DISTANT PAST

    THE TOPOLOGY OF MODULI SPACES OF LINKAGES

  • On the moduli space of polygons in the Euclidean plane, (with M.Kapovich)
    • JDG  42 (1995).  A postscript version of this article is available here.

  • Universality theorems for linkages and arrangements, (with M.Kapovich)
    • Topology 35 (1996). A postscript version of this article is available here.
     

     

    THE SYMPLECTIC GEOMETRY OF MODULI SPACES OF N-GON LINKAGES

    ( In the three-dimensional model spaces of constant curvature)
     
  • The symplectic geometry of polygons in Euclidean space (with M.Kapovich)
    • JDG. 44 (1996). A postscript version of this article is available here.
     
  • The symplectic geometry of polygons in hyperbolic 3-space (with M.Kapovich and T.Treloar).
    • Asian J. of Math.  4 (2000), (papers dedicated to the memory of K. Kodaira).  A postscript version of this article is available here.

  • The symplectic geometry of polygons in the 3-sphere (by T.Treloar)
    • Canadian J. of Math. 54 (2002). A postscript version of this article is available here.

    (In the space of positive definite Hermitian matrices)

  • The moduli space of weighted configurations on projective space (with H. Flaschka).
    • Canadian J. of Math. 57(2005). A postscript version of this article is available here.

    THE GENERALIZED TRIANGLE INEQUALITIES IN SYMMETRIC SPACES AND EUCLIDEAN BUILDINGS AND THE CONNECTION WITH THE STRUCTURE CONSTANTS OF REPRESENTATION RINGS AND HECKE ALGEBRAS

  • Convex functions on symmetric spaces and geometric invariant theory for spaces of weighted configurations
    • on flag manifolds, (with M. Kapovich and B. Leeb).  A pdf version of this article is available here.

  • Polygons in symmetric spaces and Euclidean buildings (with Misha Kapovich and Bernhard Leeb)   A pdf version of this article is available here.

  • The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
    • (with M. Kapovich and B. Leeb).  A pdf version of this article is available here.

  • A path model for geodesics in Euclidean buildings and its applications to representation theory
    • (with M. Kapovich ).  A pdf version of this article is available here.

  • Saturation and irredundancy for Spin(8)
    • (with M. Kapovich and S. Kumar). A pdf version of this article is available here.

  • Misha Kapovich's Madrid ICM talk (2006)
    • A pdf version of this article is available here.
     

     
     
     

               DEFORMATIONS OF REPRESENTATIONS OF FINITELY GENERATED GROUPS
     

  • On the deformation theory of representations of fundamental groups of compact hyperbolic 3-manifolds (with

    • M. Kapovich),  Topology 35 (1996).  A postscript version of this articles is available here.
     
  • On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth algebraic varieties, (with M. Kapovich), Publ. Math. IHES, 88 (1998)  A postscript version of this article is available here.
    		•

     

     
     

               FLAT CONNECTIONS AND REPRESENTATIONS OF GENERALIZED ARTIN GROUPS OF LIE TYPE
     

  • Quantization of bending deformations of polygons in Euclidean 3-space, hypergeometric integrals and the Gassner representation (with M.Kapovich).

    • Canad. Math. Bull. 44 (2001). A postscript version of this article is available here.
     
  • Casimir operators and monodromy representations of generalized braid groups (with Valerio Toledano Laredo)

    • Transformation Groups, 10, 2005. A postscript version of this article is available here.

     

               THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE

      Over the last four years I have been engaged in a collaboration with Ben Howard, Andrew Snowden and Ravi Vakil. This HMSV collaboration has resulted in six papers culminating with the paper below "The ideal of relations for the moduli space of n points on the line".

    Our first paper computed the equations of the moduli spaace. It was published in Duke Math J., Vol. 46, 2009, 175-226.

  • The equations for the moduli space of n points on the line
    A pdf version of this article is available here.

    • We have just solved the much harder problem of finding the relations between the generating invariants found by Kempe in 1894.
  • The ideal of relations for the moduli space of n points on the line (with Ben Howard, Andrew Snowden and Ravi Vakil)
    • A pdf version of this article is available here.

    The hard part of the proof is to reduce to the eight-point case which we solved in the paper
  • The ring of projective invariants of eight points on the line via representation theory.
    A pdf version of this article is available here

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