List of Publications (Ezra Getzler)
- Pseudodifferential operators on
supermanifolds and the Atiyah-Singer index theorem,
Comm. Math. Phys. 92 (1983), 163-178.
- A short proof of the Atiyah-Singer index
theorem, Topology 25 (1986), 111-117.
- 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.
- Degree theory for Wiener maps,
J. Func. Anal. 68 (1986),
- The degree of the Nicolai
map, J. Func. Anal. 74 (1987), 121-138.
- The degree theory of the Nicolai map, in "VIIIth
international congress on mathematical physics (Marseille, 1986)"
World Scientific, Singapore, 1987, pp. 431-438.
- (with J. L. Brylinski) The
homology of algebras of pseudo-differential symbols and the
non-commutative residue, K-Theory 1 (1987), 385-403.
- 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.
asymptotiques de Demailly pour les fibrés vectoriels,
C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), 475-478.
- A Demailly inequality for
strictly pseudo-convex CR manifolds J. Differential
Geom. 29 (1989), 231-244.
- Cyclic homology and the
Beilinson-Manin-Schechtman central extension
Proc. Amer. Math. Soc. 104 (1989), 729-734.
- Dirichlet forms on loop space
Bull. Sci. Math. (2) 113 (1989), 151-174.
- 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.
- 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,
- (with A. Szenes) On the Chern character of
theta-summable Fredholm modules J. Func. Anal. 84
- (with J.D.S. Jones) A∞-algebras and the cyclic bar
complex Illinois J. Math. 34 (1989), 256-283.
- (with J.D.S. Jones and S. Petrack) Differential forms on loop space and the cyclic bar
30 (1991), 339-371.
- (with N. Berline and M. Vergne) "Heat
Kernels and Dirac Operators," Grundlehren 298,
Springer-Verlag, Berlin-Heidelberg-New York, 1992. Grundlehren Text
- (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.
- 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.
- (with J. Block) Equivariant cyclic
homology and equivariant differential forms Ann. Sci. Ecole
Normale Sup. (4) 27 (1994), 493-527.
- (with J.D.S. Jones) The cyclic homology of
crossed product algebras J. Reine
Angew. Math. 445 (1993), 161-174.
- (with J. Block and J.D.S Jones) The cyclic
homology of crossed product algebras. II. Topological
algebras J. Reine Angew. Math. 466 (1995),
- 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.
- The odd Chern character in cyclic
homology and spectral flow Topology 32 (1993),
Batalin-Vilkovisky algebras and two-dimensional topological field
theories Comm. Math. Phys. 159 (1994), 265-285.
Two-dimensional topological gravity and equivariant
cohomology Comm. Math. Phys. 163 (1994), 473-489.
- The equivariant Chern character for non-compact
Lie groups Adv. Math. 109 (1994), 88-107.
- The Bargmann representation,
generalized Dirac operators and the index of pseudodifferential
Rn in "Symplectic geometry and
quantization," Contemp. Math. 179, Amer. Math. Soc.,
Providence, RI, 1994, pp. 63-81.
- The Atiyah-Bott fixed point
formula in "Raoul Bott: collected papers, vol. 2,"
Birkhäuser, Boston, 1994, pp. xxxi-xxxiii.
- Manin pairs
and topological field theory Ann. Phys. 237 (1995),
- (with M.M. Kapranov) Cyclic operads and cyclic
homology, in "Geometry, topology and physics," International
Press, Cambridge, MA, 1995, pp. 167-201.
- Operads and
moduli spaces of genus 0 Riemann surfaces, in "The moduli
space of curves," Progr. Math.
129, Birkhäuser, Boston, 1995, pp. 199-230.
Intersection theory on M1,4 and elliptic Gromov-Witten
invariants J. Amer. Math. Soc. 10 (1997), 973-998.
- (with M.M. Kapranov) Modular operads
Compositio Math. 110 (1998), 65-126.
semi-classical approximation for modular operads
Commun. Math. Phys. 198 (1998), 481-492.
- (with R. Pandharipande) Virasoro constraints and
the Chern classes of the Hodge bundle Nucl. Phys. B530
Resolving mixed Hodge structures of configuration spaces Duke
J. Math. 96 (1999),
recursion relations in genus 2 In "Integrable systems and
algebraic geometry (Kobe/Kyoto, 1997)," World Sci. Publishing, River
Edge, NJ, 1998, pp. 73-106.
- (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.
- 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,
- 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.)
- (with T. Eguchi and C.-S. Xiong) Topological gravity in
genus 2 with two primary fields Adv. Theor. Math. Phys.
4 (2000), 981-998.
of Yu. I. Manin, "Frobenius manifolds, quantum cohomology,
and moduli spaces," Bull. Amer. Math. Soc. 38 (2001), 101-108.
- The Toda
conjecture In "Symplectic geometry and mirror symmetry
(KIAS, Seoul, 2000)," eds. K. Fukaya et al., World Scientific,
Singapore, 2001, pp. 51-79.
characteristics of local systems on M2 Compositio
Math. 132 (2002),
- (with A. Okounkov and R. Pandharipande) Multipoint series of
Gromov-Witten invariants of CP1
Lett. Math. Phys. 62 (2002),
- The equivariant Toda lattice.
Publ. RIMS, Kyoto 40 (2004), 507-536.
- 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.
- (with R. Pandharipande) The Betti
numbers of M0,n(r,d) J. Alg. Geometry
15 (2006), 709-732.
X. Z. Cheng) Transferring
homotopy commutative algebraic structures J. Pure
Appl. Alg. 212 (2008), 2535-2542.
- Lie theory
for nilpotent L∞ algebras Ann. of
Math. 170 (2009), 271-301.
revisited In "Algebra, arithmetic, and geometry: in honor of
Yu. I. Manin," Vol. I, 675-698, Progr. Math. 269 Birkhäuser
Boston, Boston, MA, 2009.
filtration of open/closed topological field theory.
Math. Forschungsinst. Oberwolfach, Report No. 25/2010, "Geometry,
Quantum Fields and String: Categorical Aspects," 1507--1511.
- (with K. Behrend)
Geometric higher groupoids and categories. To
appear, Bismut Festchrift, Progress in Mathematics.
- The derived Maurer-Cartan
locus. L'Enseignement Mathématique (2) 62 (2016), 261--284.
The Batalin-Vilkovisky formalism of the spinning particle.
J. High Energy Phys. (2016) 2016:17.
- The spinning
particle with curved target. To appear, Commun. Math. Phys.
Unpublished Papers and Preprints
Operads, homotopy algebra, and iterated integrals for double loop
spaces University of Warwick preprint. March,
homology groups of some two-step nilpotent Lie algebras associated to
symplectic vector spaces
- (with E. Looijenga) The Hodge polynomial of
- Higher derived