Multiple zeta values in deformation quantization

DOI10.1007/s00222-020-00970-xzbMath1454.11161arXiv1812.11649OpenAlexW2906988765MaRDI QIDQ2006707

Erik Panzer, Peter Banks, Brent Pym

Publication date: 12 October 2020

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11649

zbMATH Keywords

multiple zeta valuesdeformation quantization of Poisson bracketsKontsevich's integrals

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Deformation quantization, star products (53D55) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (6)

Quantizations of local surfaces and rebel instantons ⋮ On the Moyal star product of resurgent series ⋮ A cell decomposition of the Fulton MacPherson operad ⋮ Hyperlogarithmic functional equations on del Pezzo surfaces ⋮ Strict quantization of polynomial Poisson structures ⋮ The Expansion ⋆ mod ō (ℏ⁴) and Computer-Assisted Proof Schemes in the Kontsevich Deformation Quantization

Uses Software

• nauty
• Traces
• HyperInt

Cites Work

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• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• The multiple zeta value data mine
• Formality theorem for Hochschild cochains via transfer
• Kontsevich deformation quantization and flat connections
• The explicit equivalence between the standard and the logarithmic star product for Lie algebras. II.
• Logarithms and deformation quantization
• The homotopy braces formality morphism
• The Kontsevich weight of a wheel with spokes pointing outward
• A comparison between Rieffel's and Kontsevich's deformation quantizations for linear Poisson tensors
• Multiple harmonic series
• Operads and motives in deformation quantization
• The cohomology ring of the colored braid group
• Mixed Tate motives and multiple zeta values
• A proof of the Tsygan formality conjecture for chains.
• A path integral approach to the Kontsevich quantization formula.
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• On the coefficients of the Alekseev-Torossian associator
• Three-mass triangle integrals and single-valued polylogarithms
• Deformation quantization of Poisson manifolds
• Single-valued multiple polylogarithms in one variable
• Graphical functions and single-valued multiple polylogarithms
• Stable cohomology of polyvector fields
• Feynman integrals and iterated integrals on moduli spaces of curves of genus zero
• M. Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra
• Practical graph isomorphism. II.
• Closed string amplitudes as single-valued open string amplitudes
• Graph homology of the moduli space of pointed real curves of genus zero
• On the chain-complex of a fibration
• KONTSEVICH'S UNIVERSAL FORMULA FOR DEFORMATION QUANTIZATION AND THE CAMPBELL–BAKER–HAUSDORFF FORMULA
• Characteristic Classes in Deformation Quantization: Fig. 1.
• Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
• Iterated path integrals
• Le produit star de Kontsevich sur le dual d'une algèbre de Lie nilpotente
• Multiple $\zeta$-motives and moduli spaces $\overline{\mathcal{M}}_{0,n}$
• Special values of multiple polylogarithms
• Algebraic relations for multiple zeta values
• Operads and moduli spaces of genus $0$ Riemann surfaces
• On the (Ir)rationality of Kontsevich Weights
• Closed strings as single-valued open strings: a genus-zero derivation
• Kontsevich’s integral for the Kauffman polynomial
• SINGLE-VALUED MOTIVIC PERIODS AND MULTIPLE ZETA VALUES
• Vanishing of the Kontsevich integrals of the wheels
• Irrationality of infinitely many values of the zeta function at odd integers.

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