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 …

Abstract We propose the Volume Conjecture for the relative Reshetikhin–Turaev invariants
of a closed oriented 3-manifold with a colored framed link inside it whose asymptotic …

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 …

In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces.
When the separating surface is decorated by a spherical fusion category, we obtain …

The asymptotic behavior of quantum $6 j $-symbols is closely related to the volume of
truncated hyperideal tetrahedra\,\cite {C}, and plays a central role in understanding the …

A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth
gives a 4-tensor appearing in a recent work of Bultinck–Mariën–Williamson–Şahinoğlu …

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 …

The representation category of a conformal net is a unitary modular tensor category. We
investigate the reconstruction program: whether all unitary modular tensor categories are …

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