Papers and Preprints

• Index theory and noncommutative geometry: a survey. (joint with E. van Erp)

• Comparison of spaces associated to DGLA via higher holonomy. (joint with P. Bressler, R. Nest and B. Tsygan)

• Index pairing with Alexander-Spanier cocycles. (joint with H. Moscovici)
  (Journal of Geometry and Physics, Volume 133 (2018))

• Fibrations and higher products in cohomology. (joint with Z. Xie)
  (Journal of Topology and Analysis, Vol. 11, No. 01, pp. 135-147 (2019))

• Generalized Euler classes, differential forms and commutative DGAs. (joint with D. Sullivan and Z. Xie)
  (Journal of Topology and Analysis, Vol. 11, No. 01, pp. 109-118 (2019))

• Regularity of a general equilibrium in a model with infinite past and future. (joint with A. Rubinchik)
  (Journal of Mathematical Economics, Volume 74(2018), pp. 35-45. )

• Equivariant algebraic index theorem. (joint with R. Nest and N. de Kleijn)
  (Journal of the Institute of Mathematics of Jussieu )

• The Higher Twisted Index Theorem For Foliations. (joint with M.-T. Benameur and E. Leichtnam)
  (Journal of Functional Analysis Volume 273 (2017), no. 2, pp. 496–558.

• A Hilbert bundle description of differential K-theory. (joint with J. Lott)
  ( Advances in Mathematics volume 328 (2018))

• On quasi-classical limits of DQ-algebroids. (joint with P. Bressler, R. Nest and B. Tsygan)
  ( Compositio Mathematica. Volume 153, Issue 1, 2017, pp. 41-67)

• A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings. (joint with H. Moriyoshi, P. Piazza)
  (Journal of Noncommutative Geometry. Volume 10, Issue 1, 2016, pp. 265–306)

• On the spectral flow for Dirac operators with local boundary conditions. (joint with M. Lesch )
  ( Int. Math. Res. Notices.Volume 2015, Issue 17, pages 8036-8051)

• Formality theorem for gerbes. (joint with P. Bressler, R. Nest and B. Tsygan)
  ( Advances in Mathematics volume 273 (2015), pages 215-241)

• Deligne groupoid revisited. (joint with P. Bressler, R. Nest and B. Tsygan)
  ( Theory and Applications of Categories volume 30, (2015), No. 29, pages 1001-1016)

• Formality for algebroids I: Nerves of two-groupoids.. (joint with P. Bressler, R. Nest and B. Tsygan)
  

• The index of a transverse Dirac-type operator: the case of abelian Molino sheaf.(joint with J. Lott)
  ( Journal für die reine und angewandte Mathematik volume 678 (2013), pages 125--162)

• Local index theorem for projective families. (joint with M.-T. Benameur)
  (In Perspectives on Noncommutative Geometry, volume 61 of Fields Institute Communications. AMS, 2011, pages 1-28 )

• Deformations of algebroid stacks. (joint with P. Bressler, R. Nest and B. Tsygan)
  ( Advances in Mathematics volume 226 (2011), issue 4, pages 3018–3087)

• Chern character for twisted modules. (joint with P. Bressler, R. Nest and B. Tsygan)
  (In Geometry and Dynamics of Groups and Spaces, volume 265 of Progress in Mathematics. Birkhäuser, 2008, pages 309-324 )

• Deformation of gerbes on smooth manifolds. (joint with P. Bressler, R. Nest and B. Tsygan)
  (In K-Theory and Noncommutative Geometry , EMS Series of Congress Reports, 2008, pages 349-393 .)

• Deformations of Azumaya algebras. (joint with P. Bressler, R. Nest and B. Tsygan)
  (In Actas del XVI Coloquio Latinoamericano de Algebra ,
  Biblioteca de la Revista Matemática Iberoamericana, 2007, pages 131--152)

• Deformation quantization of gerbes. (joint with P. Bressler, R. Nest and B. Tsygan)
  ( Advances in Mathematics volume 214 (2007), issue 2, pages 230-266)

• Bivariant Chern character and longitudinal index.
  ( Journal of Functional Analysis volume 237 (2006), issue 1, pages 105--134)

• Local index theory over foliation groupoids. (joint with J. Lott)
  ( Advances in Mathematics volume 204 (2006), issue 2, pages 413--447)

• Local index theory over etale groupoids. (joint with J. Lott)
  ( Journal für die reine und angewandte Mathematik volume 560 (2003), pages 151--198 )

• Secondary characteristic classes and cyclic cohomology of Hopf algebras.
  (Topology volume 41 (2002), issue 5, pages 993-1016)

• Characters of cycles, equivariant characteristic classes and Fredholm modules.
  (Communications in Mathematical Physics, volume 208 (1999), number 1, pages 1-23)

• Explicit formulae for characteristic classes in noncommutative geometry.
  Ph.D. thesis, OSU, 1999

• Chern classes in Alexander-Spanier cohomology.
  (K-theory volume 15 (1998), number 3, pages 253-268)