This is a transcript of a series of eight lectures, 90 min each, held at IMSc Chennai, India
from 5–24 January 2015. We give basic definitions, properties and examples of compact …

We prove that the von Neumann algebras of quantum permutation groups and quantum
reflection groups have the Connes embedding property. We do this by establishing several …

Quantum permutations arise in many aspects of modern “quantum mathematics”. However,
the aim of this article is to detach these objects from their context and to give a friendly …

Given a quantum permutation group G⊂ SN+, with orbits having the same size K, we
construct a universal matrix model π: C (G)→ MK (C (X)), having the property that the images …

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 introduce a Sinkhorn-type algorithm for producing quantum permutation matrices
encoding symmetries of graphs. Our algorithm generates square matrices whose entries are …

Abstract In 2019, Jung–Weber gave an example of a concrete magic unitary M, which
defines a C*-algebraic model of the quantum permutation group S 4+. We show with the …

Using a suitably noncommutative flat matrix model, it is shown that the quantum permutation
group has free orbitals: that is, a monomial in the generators of the algebra of functions can …

This is an introduction to graph theory, from a geometric viewpoint. A finite graph $ X $ is
described by its adjacency matrix $ d\in M_N (0, 1) $, which can be thought of as a kind of …

A complex Hadamard matrix is a square matrix H∈ MN (C) whose entries are on the unit
circle,| Hij|= 1, and whose rows and pairwise orthogonal. The main example is the Fourier …