Noncommutative Batalin-Vilkovisky geometry and matrix integrals

@article{Barannikov2010NoncommutativeBG,
  title={Noncommutative Batalin-Vilkovisky geometry and matrix integrals},
  author={S. Barannikov},
  journal={Comptes Rendus Mathematique},
  year={2010},
  volume={348},
  pages={359-362}
}
  • S. Barannikov
  • Published 30 December 2009
  • Mathematics
  • Comptes Rendus Mathematique
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References

SHOWING 1-8 OF 8 REFERENCES
Modular Operads
We develop a \higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the deenition. We study a functor F on the category of modular operads, the Feynman
Intersection theory on the moduli space of curves and the matrix airy function
We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical
Quantum Fields and Strings: A Course for Mathematicians
Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics. In
Feynman Diagrams and Low-Dimensional Topology
We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, non-commutative geometry and several kinds of “topological physics.”
Supersymmetric matrix integrals and model
  • Supersymmetric matrix integrals and model
  • 2009
rue d'Ulm 75230, Paris, France E-mail address : sergueibar@gmail.com hal-00102085
  • rue d'Ulm 75230, Paris, France E-mail address : sergueibar@gmail.com hal-00102085
  • 2009
The superalgebra Q(n), the odd trace, and the odd determinant
  • Dokl. Bolg. Akad. Nauk
  • 1982
Modular operads and non-commutative Batalin-Vilkovisky geometry. Preprint MPIM(Bonn) 2006-48
  • IMRN
  • 2007