Motivated by the three-dimensional topological field theory/two-dimensional conformal field
theory (CFT) correspondence, we study a broad class of one-dimensional quantum …

We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-
system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove …

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 introduce fusion bialgebras and their duals and systematically study their Fourier
analysis. As an application, we discover new efficient analytic obstructions on the unitary …

We introduce a pictorial approach to quantum information, called holographic software. Our
software captures both algebraic and topological aspects of quantum networks. It yields a bi …

We define a planar para algebra, which arises naturally from combining planar algebras
with the idea of Z _ N ZN para symmetry in physics. A subfactor planar para algebra is a …

Discrete subfactors include a particular class of infinite index subfactors and all finite index
ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity …

In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum
groups and characterize the minimizer which are bi-shifts of group-like projections. We also …

This paper originates from a naive attempt to establish various non-commutative Fourier
theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional …

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 …