Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the deformation theory of associative algebras, is the “Kontsevich representation” of a DGLA of graphs coming from a pre-Lie algebra structure defined by graph insertions (Gerstenhaber composition with Leibniz rule). Propert...

Recent work in perturbative quantum field theory has led to much study of the Connes-Kreimer Hopf algebra. Its (graded) dual, the Grossman-Larson Hopf algebra of rooted trees, had already been studied by algebraists. L. Foissy introduced a noncommutative version of the Connes-Kreimer Hopf algebra, which turns out to be self-dual. Using some homomorphisms defined by the author and W. Zhao, we de...

Let X be a manifold on which a discrete (pseudo)group of diffeomorphisms Γ acts, and let E be a Γ-equivariant vector bundle on X. We give a construction of cyclic cocycles on the cross product algebra C∞ 0 (X)o Γ representing the equivariant characteristic classes of E. Our formulas can be viewed as a higher-dimensional analogue of Connes’ Godbillon-Vey cyclic cocycle. An essential tool for our...

Abstract We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve nonlinear oscillations of partial differential equation (PDE) and approximate with high-order accuracy large class under lower regularity assumptions than classical techniques require. The key idea control frequency interactio...

This is a detailed survey on the QWEP conjecture and Connes’ embedding problem. Most of contents are taken from Kirchberg’s paper [Invent. Math. 112 (1993)].

In this paper, we verify the $L^p$ coarse Baum–Connes conjecture for spaces with finite asymptotic dimension $p\in\[1,\infty)$. We also show that $K$-theory of Roe algebras is independent $p\in(1,\infty)$ dimension.