This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one
up to rank six. Among 72 possible fusion rings, 25 ones are filtered out by using …

Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial
in the case of subfactor theory) with analytic estimates. This provides interesting tools to …

We present a method to generate all fusion rings of a specific rank and multiplicity. This
method generated exhaustive lists of fusion rings up to order 9 for several multiplicities. We …

A bstract We study Galois actions on 2+ 1D topological quantum field theories (TQFTs),
characterizing their interplay with theory factorization, gauging, the structure of gapped …

In this paper, we extend a classical vanishing result of Burnside from the character tables of
finite groups to the character tables of commutative fusion rings, or more generally to a …

We study odd-dimensional modular tensor categories and maximally nonself dual (MNSD)
modular tensor categories of low rank. We give lower bounds for the ranks of modular tensor …

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras,
which unify a number of uncertainty principles on quantum symmetries, such as subfactors …

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal
subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep (PSL (2, q)) …

We introduce the triangular prism equations for fusion categories, which turn out to be
equivalent to the pentagon equations in the spherical case (up to a change of basis), but …

Conformal inclusions of chiral conformal field theories, or more generally inclusions of
quantum field theories, are described in the von Neumann algebraic setting by nets of …