List of Publications

 

  • 1. Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys. 92 (1983), 163-178.
  • 2. A short proof of the Atiyah-Singer index theorem, Topology 25 (1986), 111-117.
  • 3. The local Atiyah-Singer index theorem, in “Critical phenomena, random systems, gauge theories (Les Houches 1984)” North-Holland, Amsterdam-New York, 1986, pp. 967-974.
  • 4. Degree theory for Wiener maps, J. Func. Anal. 68 (1986), 388-403.
  • 5. The degree of the Nicolai map, J. Func. Anal. 74 (1987), 121-138.
  • 6. The degree theory of the Nicolai map, in “VIIIth international congress on mathematical physics (Marseille, 1986)” World Scientific, Singapore, 1987, pp. 431-438.
  • 7. (with J. L. Brylinski) The homology of algebras of pseudo-differential symbols and the non-commutative residue, K-Theory 1 (1987), 385-403.
  • 8. A heat equation approach to Boutet de Monvel’s index theorem for Toeplitz operators, in “Miniconference on harmonic analysis and operator algebras (Canberra, 1987),” Proc. Centre Math. Anal. Austral. Nat. Univ. 15, Austral. Nat. Univ., Canberra, 1987, pp. 55-65.
  • 9. Inégalités asymptotiques de Demailly pour les fibrés vectoriels, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), 475-478.
  • 10. A Demailly inequality for strictly pseudo-convex CR manifolds, J. Differential Geom. 29 (1989), 231-244.
  • 11. Cyclic homology and the Beilinson-Manin-Schechtman central extension, Proc. Amer. Math. Soc. 104 (1989), 729-734.
  • 12. Dirichlet forms on loop space, Bull. Sci. Math. (2) 113 (1989), 151-174.
  • 13. The Thom class of Mathai and Quillen and probability theory, in “Stochastic Analysis and Applications (Lisbon, 1989)” Progr. Probab. 26, Birkhäuser, Boston, 1991, pp. 111-122.
  • 14. An extension of Gross’s log-Sobolev inequality for the loop space of a compact Lie group, in “Probability Models in Mathematical Physics,” World Scientific, Singapore, 1991, pp. 73-97.
  • 15. (with A. Szenes) On the Chern character of theta-summable Fredholm modules, J. Func. Anal. 84 (1989), 343-357.
  • 16. (with J. D. S. Jones) A∞-algebras and the cyclic bar complex, Illinois J. Math. 34 (1989), 256-283.
  • 17. (with J. D. S. Jones and S. Petrack) Differential forms on loop space and the cyclic bar complex, Topology 30 (1991), 339-371.
  • 18. (with N. Berline and M. Vergne) “Heat Kernels and Dirac Operators,” Grundlehren 298, Springer-Verlag, Berlin-Heidelberg-New York, 1992. Grundlehren Text Edition, 2003.
  • 19. (with J. Block) Quantization of foliations, in “Proceedings of the XXth International Conference on Differential Geometric Methods in Physics (New York, 1991)” World Scientific, Singapore, 1992, pp. 471-487.
  • 20. Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology, in “Quantum deformations of algebras and their representations,” Israel Math. Conf. Proc. 7 (1993), pp. 65-78.
  • 21. (with J. Block) Equivariant cyclic homology and equivariant differential forms, Ann. Sci. Ecole Normale Sup. (4) 27 (1994), 493-527.
  • 22. (with J. D. S. Jones) The cyclic homology of crossed product algebras, J. Reine Angew. Math. 445 (1993), 161-174.
  • 23. (with J. Block and J. D. S Jones) The cyclic homology of crossed product algebras. II. Topological algebras, J. Reine Angew. Math. 466 (1995), 19-25.
  • 24. Cyclic homology and the Atiyah-Patodi-Singer index theorem, in “Index theory and operator algebras,” Contemp. Math. 148, Amer. Math. Soc., Providence, RI, 1993, pp. 19-45.
  • 25. The odd Chern character in cyclic homology and spectral flow, Topology 32 (1993), 489-507.
  • 26. Batalin-Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994), 265-285.
  • 27. Two-dimensional topological gravity and equivariant cohomology, Comm. Math. Phys. 163 (1994), 473-489.
  • 28. The equivariant Chern character for non-compact Lie groups, Adv. Math. 109 (1994), 88-107.
  • 29. The Bargmann representation, generalized Dirac operators and the index of pseudodifferential operators on Rn, in “Symplectic geometry and quantization,” Contemp. Math. 179, Amer. Math. Soc., Providence, RI, 1994, pp. 63-81.
  • 30. The Atiyah-Bott fixed point formula, in “Raoul Bott: collected papers, vol. 2,” Birkhäuser, Boston, 1994, pp. xxxi-xxxiii.
  • 31. Manin pairs and topological field theory, Ann. Phys. 237 (1995), 161-201.
  • 32. (with M. M. Kapranov) Cyclic operads and cyclic homology, in “Geometry, topology and physics,” International Press, Cambridge, MA, 1995, pp. 167-201.
  • 33. Operads and moduli spaces of genus 0 Riemann surfaces, in “The moduli space of curves,” Progr. Math. 129, Birkhäuser, Boston, 1995, pp. 199-230.
  • 34. Intersection theory on M1,4 and elliptic Gromov-Witten invariants, J. Amer. Math. Soc. 10 (1997), 973-998.
  • 35. (with M. M. Kapranov) Modular operads, Compositio Math. 110 (1998), 65-126.
  • 36. The semi-classical approximation for modular operads, Commun. Math. Phys. 198 (1998), 481-492.
  • 37. (with R. Pandharipande) Virasoro constraints and the Chern classes of the Hodge bundle, Nucl. Phys. B530 (1998), 701-714.
  • 38. Resolving mixed Hodge structures of configuration spaces, Duke J. Math. 96 (1999), 175-203.
  • 39. Topological recursion relations in genus 2, in “Integrable systems and algebraic geometry (Kobe/Kyoto, 1997),” World Sci. Publishing, River Edge, NJ, 1998, pp. 73-106.
  • 40. (edited with M.M. Kapranov) “Higher category theory. (Papers from the Workshop on Higher Category Theory and Physics held at Northwestern University, Evanston, IL, March 28-30, 1997.)” Contemp. Math. vol. 230. AMS, Providence, RI, 1998.
  • 41. The Virasoro conjecture for Gromov-Witten invariants, in “Algebraic Geometry — Hirzebruch 70 (Warsaw, 1998),” Contemp. Math., 241, Amer. Math. Soc., Providence, RI, 1999, pp. 147-176,
  • 42. A Darboux theorem for Hamiltonian operators in the formal calculus of variations, Duke J. Math. 111 (2002), 535-560.
    (Here are the two letters of Deligne to Breen on 2-groupoids and differential graded Lie algebras.)
  • 43. (with T. Eguchi and C.-S. Xiong) Topological gravity in genus 2 with two primary fields, Adv. Theor. Math. Phys. 4 (2000), 981-998.
  • 44. Review of Yu. I. Manin, “Frobenius manifolds, quantum cohomology, and moduli spaces,” Bull. Amer. Math. Soc. 38 (2001), 101-108.
  • 45. The Toda conjecture, In “Symplectic geometry and mirror symmetry (KIAS, Seoul, 2000),” eds. K. Fukaya et al., World Scientific, Singapore, 2001, pp. 51-79.
  • 46. Euler characteristics of local systems on M2, Compositio Math. 132 (2002), 121-135.
  • 47. (with A. Okounkov and R. Pandharipande) Multipoint series of Gromov-Witten invariants of CP1, Lett. Math. Phys. 62 (2002), 159-172.
  • 48. The equivariant Toda lattice, Publ. RIMS, Kyoto 40 (2004), 507-536.
  • 49. The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants, in “Frobenius manifolds,” Aspects Math., E36, Vieweg, Wiesbaden, 2004, pp. 45-89.
  • 50. (with R. Pandharipande) The Betti numbers of M0,n(r,d), J. Alg. Geometry 15 (2006), 709-732.
  • 51. (with X. Z. Cheng) Transferring homotopy commutative algebraic structures, J. Pure Appl. Alg. 212 (2008), 2535-2542.
  • 52. Lie theory for nilpotent L∞ algebras, Ann. of Math. 170 (2009), 271-301.
  • 53. Operads revisited, in “Algebra, arithmetic, and geometry: in honor of Yu. I. Manin,” Vol. I, 675-698, Progr. Math. 269 Birkhäuser Boston, Boston, MA, 2009.
  • 54. A filtration of open/closed topological field theory, Math. Forschungsinst. Oberwolfach, Report No. 25/2010, “Geometry, Quantum Fields and String: Categorical Aspects,” 1507-1511.
  • 55. (with K. Behrend) Geometric higher groupoids and categories, in “Geometry, Analysis and Probability: In Honor of Jean-Michel Bismut.” Progr. Math., 310, eds. J.-B. Bost et al., Birkhäuser Boston, Boston, MA, 2017, pp. 1-45.
  • 56. The derived Maurer-Cartan locus, L’Enseignement Mathématique (2) 62 (2016), 261-284.
  • 57. The Batalin-Vilkovisky formalism of the spinning particle, J. High Energy Phys. (2016) 2016:17.
  • 58. The spinning particle with curved target, Commun. Math. Phys. 352 (2017), no. 1, 185-199.
  • 59. Covariance in the Batalin-Vilkovisky formalism and the Maurer-Cartan equation for curved Lie algebras, Lett. Math. Physics 109(1) (2018), 187-224.
  • 60. (with S.W. Pohorence) Covariance of the classical Brink-Schwarz superparticle, Adv. Theor. Math. Phys. 23 (2019).

Unpublished Papers and Preprints

  • 1. (with J. D. S. Jones) Operads, homotopy algebra, and iterated integrals for double loop spaces, University of Warwick preprint. March, 1994.
  • 2. The homology groups of some two-step nilpotent Lie algebras associated to symplectic vector spaces
  • 3. (with E. Looijenga) The Hodge polynomial of M3,1
  • 4. Higher derived brackets