Research page

Research interests

• Homological algebra and higher algebraic structures, such as Categories, Stacks, Gerbes, and their differential geometry.
• Moduli of Riemann Surfaces and algebraic curves, Teichmüller spaces and related structures.
• Mathematical Physics, in particular algebraic structures related to Conformal Field Theory and String Theory and their applications to Algebraic Geometry and Complex Analysis.

Recent preprints and publications

• Notes on Weak Units of Picard 1- and 2-Stacks (with A. Emin Tatar)
• Butterflies II: Torsors for 2-group stacks (with Behrang Noohi)
  Advances in Mathematics 225 (2010), 922–976 DOI: 10.1016/j.aim.2010.03.011
  Local copies: DVI PS PDF
• Butterflies I: Morphisms of 2-group stacks (with Behrang Noohi)
  Advances in Mathematics 221 (2009), 687–773 DOI: 10.1016/j.aim.2008.12.014
  Local copies: DVI PS PDF
• 2-gerbes bound by complexes of gr–stacks, and cohomology
  Journal of Pure and Applied Algebra 212 (2008), 994–1038 DOI: 10.1016/j.jpaa.2007.07.020
  Local copies: DVI PS PDF
• Hermitian-holomorphic Deligne cohomology, Deligne pairing for singular metrics, and hyperbolic metrics
  Int. Mathematics Research Notices 17 (2005), 1015–1046.
  (Local copies in DVI PS PDF)
• Hermitian-holomorphic (2)-gerbes and tame symbols
  Journal of Pure and Applied Algebra 200 (2005), 97–135.
  (Local copies in DVI PS PDF)
• On hermitian-holomorphic classes related to uniformization, the dilogarithm and the Liouville action
  Commun. Math. Phys. 251 (2004) 27–64
  (Local copies in DVI PS PDF)
• Homological algebra of multivalued action functionals
  Letters in Mathematical Physics 60 (2002) 47-58
• Generating Functional in CFT on Riemann Surfaces II: Homological Aspects (with L. A. Takhtajan)
  Commun. Math. Phys. 227 (2002) 303–348