Kenji Ueno

• Director at Yokkaichi University

In Andersen and Ueno (J Knot Theory Ramif 16:127–202, 2007) we constructed the vacua modular functor based on the sheaf of vacua theory developed in Tsuchiya et al. (Adv Stud Pure Math 19:459–566, 1989) and the abelian analog in Andersen and Ueno (Int J Math 18:919–993, 2007). We here provide an explicit isomorphism from the modular functor underly...

In this chapter we examine classroom practice issues related to teachers provid- ing mathematical challenges in their everyday classrooms. We examine how challenging mathematics can become the essence of mathematics classrooms, how challenging mathematics can be designed for the everyday classroom and how classroom artifacts and practices can be de...

The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichm\"uller space of an oriented pointed...

We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the S-matrix in genus one with one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assume the modular functor in question has duality or is...

The transition from wasan to yozan (western mathematics) was smoothly done after the Meiji government chose western mathematics as a subject of elementary education. But soroban was very popular until recently. For wasan mathematicians it was not difficult to learn the elementary parts of western mathematics but they missed the importance of logica...

We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n)-representations, for any fixed integer $n \geq 2$. In the Pseudo-Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) SU(2)-TQFT representation matrices. It follows th...

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions...

The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichm\"uller space of an oriented pointed...

It is well-known that abelian conformal field theory has a rich arithmetic structure (see, for example [DKK], [KSU1], [KSU2], [KSU3]). It is natural to ask whether this is also the case for non-abelian conformal field theory. As a first step to study arithmetic properties of non-abelian conformal field theory, in the present paper we shall study th...

this paper we shall study the Neron-Severi group for torus quasi bundles over curves. Firstly, we study the case of torus principal bundles X

This chapter focuses on the conformal field theory (CFT) on universal family of stable curves with gauge symmetries. CFT has not only useful application to string theory and two-dimensional critical phenomena but also has beautiful and rich mathematical structure, and it has interested many mathematicians. CFT is characterized by infinite-dimension...

We introduce a formal group naturally associated with algebraic curves. The formal group is isomorphic to the one obtained from the universal Witt scheme. The charge zero sector of the boson Fock space is regarded as the coordinate ring of the formal group. Using this structure, we can give tau functions. We also define new operators fn, vn (n ∈ Z,...

New formulation of bosonization is given so that it is defined over the ring Z of integers. The charge zero sector of the new boson Fock space is the completion of the coordinate ring of the universal Witt scheme. By using new bosonization, conformal field theory of free fermions over Z is given.

Introduction. The structure of algebraic threefolds with nonpositive Kodaira dimension has been studied by Ueno [8], [9] and Viehweg [10]. Their results are based on the semi-positivity theorem of the direct image sheaf of the relative canonical sheaf of a fibre space ([4]). This is a consequence of the theory of variation of Hodge structure. There...

This article contains geometrical classification of all fibres in pencils of curves of genus two, which is essentially different from the numerical one given by Ogg ([11]) and Iitaka ([7]).Given a family :XD of curves of genus two which is smooth overD=D–{0}, we define a multivalued holomorphic mapT fromD into the Siegel upper half plane of degree...

We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n) representations, for any fixed n � 2. In the Pseudo-Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) SU(2)- TQFT representation matrices. It follows that at big en...