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Some research papers (PDF files)

(2017) Collapsing in the Einstein flow, preprint
(2015) A Hilbert bundle description of differential K-theory, with Alexander Gorokhovsky, preprint

(2014) Singular Ricci flows I, with Bruce Kleiner, preprint
(2016) Note on asymptotically conical expanding Ricci solitons, with Patrick Wilson, to appear, Proc. of the AMS
(2014) An intrinsic parallel transport in Wasserstein space, to appear, Proc. of the AMS
(2014) On tangent cones in Wasserstein space, to appear, Proc. of the AMS
(2016) Ricci flow on quasiprojective manifolds II, with Zhou Zhang, J. of the Eur. Math. Soc. 18, p. 1813-1854

(2016) Ricci measure for some singular Riemannian metrics, Math. Annalen 365, p. 449-471
(2014) Geometrization of three-dimensional orbifolds via Ricci flow, with Bruce Kleiner, Asterisque 365, p. 101-177
(2014) Locally collapsed 3-manifolds, with Bruce Kleiner, Asterisque 365, p. 7-99 Minor corrections
(2014) Collapsing with a lower bound on the curvature operator, Advances in Mathematics 256, p. 291-317
(2014) Ricci flow on three-dimensional manifolds with symmetry, with Natasa Sesum, Comm. Math. Helv. 89, p. 1-32

(2013) The index of a transverse Dirac-type operator: the case of abelian Molino sheaf, with Alexander Gorokhovsky, J. Reine Angew. Math. (Crelle's Journal) 678, p. 125-162
(2012) Mean curvature flow in a Ricci flow background, Comm. Math. Phys. 313, p. 517-533
(2011) Ricci flow on quasiprojective manifolds, with Zhou Zhang, Duke Math. Journal 156, p. 87-123
(2010) Dimensional reduction and the long-time behavior of Ricci flow, Comm. Math. Helv. 85, p. 485-534
(2010) An index theorem in differential K-theory, with Dan Freed, Geometry and Topology 14, p. 903-966

(2009) Optimal transport and Perelman's reduced volume , Calc. Var. and Partial Differential Equations 36, p. 49-84
(2009) Ricci curvature for metric-measure spaces via optimal transport, with Cedric Villani, Annals of Math. 169, p. 903-991
(2008) Notes on Perelman's papers, with Bruce Kleiner, Geometry and Topology 12, p. 2587-2855
(2008) Some geometric calculations on Wasserstein space, Comm. Math. Phys. 277, p. 423-437
(2007) Optimal transport and Ricci curvature for metric-measure spaces, in Surveys in Differential Geometry, vol. XI, Metric and Comparison Geometry, eds. J. Cheeger and K. Grove, International Press, Somerville, MA, p. 229-257

(2007) Hamilton-Jacobi semigroup on length spaces and applications, with Cedric Villani, Journal de Math. Pures et Appliquees 88, p. 219-229
(2007) On the long-time behavior of type-III Ricci flow solutions, Math. Annalen 339, p. 627-666
(2007) The work of Grigory Perelman, Proc. of the ICM 2006, European Math. Soc. Publishing House, Vol. I, p. 66-77
(2007) Remark about scalar curvature and Riemannian submersions
, Proc. of the AMS 135, p. 3375-3381
(2007) Weak curvature conditions and functional inequalities, with Cedric Villani, J. of Functional Analysis 245, p. 311-333

(2006) Local index theory over foliation groupoids, with Alexander Gorokhovsky, Advances in Mathematics 204, p. 413-447
(2005) Limit sets as examples in noncommutative geometry, K-Theory 34, p. 283-326
(2003) Remark about the spectrum of the p-form Laplacian under a collapse with curvature bounded below, Proc. of the AMS 132, p. 911-918
(2003) Some geometric properties of the Bakry-Emery-Ricci tensor, Comm. Math. Helv. 78, p. 865-883
(2003) Local index theory over etale groupoids, with Alexander Gorokhovsky, J. Reine Angew. Math. (Crelle's Journal) 560, p. 151-198

(2003) Manifolds with quadratic curvature decay and fast volume growth, Math. Ann. 325, p. 525-541
(2002) Higher-degree analogs of the determinant line bundle, Comm. Math. Phys. 230, p. 41-69
(2002) Collapsing and the differential form Laplacian : the case of a smooth limit space, Duke Math. Journal 114, p. 267-306
(2002) Collapsing and Dirac-type operators, Geom. Ded. 91, p. 175-196 (special issue on Partial Differential Equations and their Applications to Geometry and Physics)
(2001) On the spectrum of a finite-volume negatively-curved manifold, Amer. J. of Math. 123, p. 185-205

(2001) The Dirac operator and conformal compactification, Internat. Math. Res. Notices 2001, No. 4, p. 171-178
(2000) On the homotopy invariance of higher signatures for manifolds with boundary, with Eric Leichtnam and Paolo Piazza, J. of Diff. Geom. 54, p. 561-633
(2000) Invariant currents on limit sets, Comm. Math. Helv. 75, p. 319-350
(2000) Manifolds with quadratic curvature decay and slow volume growth, with Zhongmin Shen, Ann. Scient. de l'Ec. Norm. Sup. (4) 33, p. 275-290
(2000) Signatures and higher signatures of $S^1$-quotients, Math. Annalen 316, p. 617-657

(2000) Delocalized $L^2$-invariants, J. Funct. Anal. 169, p. 1-31. Erratum, J. Funct. Anal. 210, p. 258. See also the paper by Michael Puschnigg which makes the erratum irrelevant.
(2000) Secondary analytic indices, in Regulators in Analysis, Geometry and Number Theory, Birkhauser Prog. in Math. Series, vol. 171, eds. A. Reznikov and N. Schappacher, Birkhauser, Boston, p. 231-293
(2000) A-hat genus and collapsing, J. of Geom. Anal. 10, p. 529-543
(1999) Diffeomorphisms and noncommutative analytic torsion, Mem. Amer. Math. Soc. 141, no. 673, viii + 56 pp.
(1999) Deficiencies of lattice subgroups of Lie groups, Bull. London Math. Soc. 31, p. 191-195

(1999) Remark about heat diffusion on periodic spaces, Proc. Amer. Math. Soc. 127, p. 1243-1249
(1998) Eta and torsion, in Symetries Quantiques (Les Houches 1995), p. 947-955
(1997) Torus bundles and the group cohomology of GL(N,Z), with J.-M. Bismut, J. Diff. Geom. 47, p. 196-236
(1997) $L^2$ cohomology of geometrically infinite hyperbolic 3-manifolds, Geom. and Funct. Anal. 7, p. 81-119
(1996) The zero-in-the-spectrum question, Enseign. Math. 42, p. 341-376

(1995) $L^2$ topological invariants of 3-manifolds, with Wolfgang Lueck, Inv. Math. 120, p. 15-60
(1995) Flat vector bundles, direct images and higher real analytic torsion, with J.-M. Bismut, J. Amer. Math. Soc. 8, p. 291-363
(1994) Equivariant analytic torsion for group actions, J. Funct. Anal. 125, p. 438-451
(1994) R/Z index theory, Comm. Anal. Geom. 2, p. 279-311
(1992) Higher eta-invariants, K-Theory 6, p. 191-233

(1992) Superconnections and higher index theory, Geom. and Funct. Anal. 2, p. 421-454
(1992) Heat kernels on covering spaces, J. Diff. Geom. 35, 471-510
(1991) Analytic torsion for group actions, J. Diff. Geom. 34, p. 431-481
(1990) Particle models and noncommutative geometry, with Alain Connes, Nucl. Phys. B Proc. Suppl. 18B, p. 29-47
(1990) Torsion constraints in supergeometry, Comm. Math. Phys. 133, p. 563-615

(1988) Real anomalies, J. Math. Phys. 29, p. 1455-1464
(1986) Supersymmetric path integrals, Comm. Math. Phys. 108, p. 605-629
(1986) Renormalization group flow for general sigma models, Comm. Math. Phys. 107, p. 165-176
(1986) Bosonization in curved spacetime, Phys. Lett. B 173, p. 319-320
(1986) Eigenvalue bounds for the Dirac operator, Pac. J. Math. 125, p. 117-126

(1985) Degrees of freedom and quantization of anomalous gauge theories, with Doug Rajaraman, Phys. Lett. B 165, p. 321-326
(1985) Effective actions and large-N limits, Comm. Math. Phys. 100, p. 133-140
(1984) The eta-function and some new anomalies, Phys. Lett. B 145, p. 179-180
(1984) The Yang-Mills collective-coordinate potential, Comm. Math. Phys. 95, p. 289-300
(1984) Vacuum charge and the eta function, Comm. Math. Phys. 93, p. 533-558


(2002) Collapsing and the differential form Laplacian : the case of a singular limit space
(2001) The geometry of supergravity torsion constraints, prepared for the 2001 Park City Mathematics Institute