Research page

Research interests

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

Recent papers and preprints

2-gerbes bound by complexes of gr–stacks, and cohomology (Local copies in 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