Our aim in this review paper is to present the applications of Connes' noncommutative
geometry to elementary particle physics. Whereas the existing literature is mostly focused on …

The seeds of this book have been planted in the far east, where I wrote lecture notes for
international schools in Tianjin, China in 2007, and in Bangkok, Thailand in 2011. I then …

Within the framework of unitary easy quantum groups, we study an analogue of Brauer's
Schur-Weyl approach to the representation theory of the orthogonal group. We consider …

We classify certain categories of partitions of finite sets subject to specific rules on the
coloring of points and the sizes of blocks. More precisely, we consider pair partitions such …

We study the 10 noncommutative spheres obtained by liberating, twisting, and liberating+
twisting the real and complex spheres SRN− 1, SCN− 1. At the axiomatic level, we show …

Within the framework of Connes' noncommutative geometry, the notion of an almost
commutative manifold can be used to describe field theories on compact Riemannian spin …

This book introduces the reader to quantum groups, focusing on the simplest ones, namely
the closed subgroups of the free unitary group. Although such quantum groups are quite …

We discuss some properties of the spectral triple. AF; HF; DF; JF; F/describing the internal
space in the noncommutative geometry approach to the Standard Model, with AF DC HM3 …

A duality principle for noncommutative cubes and spheres Page 1 J. Noncommut. Geom. 10
(2016), 1043–1081 DOI 10.4171/JNCG/254 Journal of Noncommutative Geometry © European …

We discuss the classification problem for the unitary easy quantum groups, under strong
axioms, of noncommutative geometric nature. Our main results concern the intermediate …