Noncommutative Batalin-Vilkovisky geometry and matrix integrals

  title={Noncommutative Batalin-Vilkovisky geometry and matrix integrals},
  author={S. Barannikov},
  journal={Comptes Rendus Mathematique},
  • S. Barannikov
  • Published 30 December 2009
  • Mathematics
  • Comptes Rendus Mathematique
Solving the Noncommutative Batalin–Vilkovisky Equation
Given an odd symmetry acting on an associative algebra, I show that the summation over arbitrary ribbon graphs gives the construction of the solutions to the noncommutative Batalin–Vilkovisky
Matrix De Rham Complex and Quantum A-infinity algebras
I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A∞-algebras, introduced in
The calculus of multivectors on noncommutative jet spaces
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    Journal of Geometry and Physics
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A-infinity gl(N)-equivariant matrix integrals
My talk consists of two parts. First part("genus zero"): the negative cyclic homology subspace moving inside periodic cyclic homology defines for the noncommutative varieties the analogue of the
EA-Matrix Integrals of Associative Algebras and Equivariant Localization
The EA-matrix integrals, introduced in Barannikov (Comptes Rendus Math 348:359–362, 2006), are studied in the case of graded associative algebras with odd or even scalar product. I prove that the
Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem
We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in
Minimal models of quantum homotopy Lie algebras via the BV-formalism
Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these
Matrix De Rham complex and quantum A∞−algebras
We represent the equation defining the quantum A∞−algebras introduced in ([B1],[B2]) via GL-invariant tensors on matrix spaces gl(A). This allows in particular to show that the cohomology of the
Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves M_g,n
We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves Mg,n (which, according to Penner, is controlled by the ribbon graph
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I consider the simplest examples of my equivariantly closed matrix integrals from [B06], corresponding to super associative algebras with an odd trace.


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 : hal-00102085
  • rue d'Ulm 75230, Paris, France E-mail address : 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