## 12 Citations

Solving the Noncommutative Batalin–Vilkovisky Equation

- Mathematics
- 2013

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

- Mathematics
- 2014

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

- MathematicsJournal of Geometry and Physics
- 2018

A-infinity gl(N)-equivariant matrix integrals

- Mathematics
- 2010

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

- MathematicsArnold Mathematical Journal
- 2019

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

- Mathematics
- 2021

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

- MathematicsJournal of Mathematical Physics
- 2018

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

- Mathematics
- 2009

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

- Mathematics
- 2015

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…

Higher dimensional matrix Airy functions and equivariant cohomology

- Mathematics
- 2010

I consider the simplest examples of my equivariantly closed matrix integrals from [B06], corresponding to super associative algebras with an odd trace.

## References

SHOWING 1-8 OF 8 REFERENCES

Modular Operads

- Mathematics
- 1994

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

- Mathematics
- 1992

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

- Physics
- 1999

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

- Mathematics, Physics
- 1994

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