We present a 3D topological picture-language for quantum information. Our approach
combines charged excitations carried by strings, with topological properties that arise from …

Quon language is a 3D picture language that we can apply to simulate mathematical
concepts. We introduce the surface algebras as an extension of the notion of planar …

In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion
categories. We prove the complete positivity of the comultiplication for subfactors and derive …

We give an overview of our philosophy of pictures in mathematics. We emphasize a
bidirectional process between picture language and mathematical concepts: abstraction and …

We introduce block maps for subfactors and study their dynamic systems. We prove that the
limit points of the dynamic system are positive multiples of biprojections and zero. For the ℤ …

In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which
allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary fusion …

We explicitly construct a (unitary) $\mathbb {Z}/2\mathbb {Z} $ permutation gauging of a
(unitary) modular category $\mathcal {C} $. In particular, the formula for the modular data of …

For a vertex operator algebra $ V $, we construct an explicit isomorphism between the space
of genus-0 conformal blocks associated to permutation-twisted $ V^{\otimes n} $-modules …

A modular tensor category is a non-degenerate ribbon finite tensor category. And a ribbon
factorizable Hopf algebra is exactly the Hopf algebra whose finite-dimensional …

We focus on the problem of producing new modular tensor categories from Hopf algebras.
To do this, we first give a general method to construct factorizable Hopf algebras. Then we …