Related papers: On mapping class groups and their TQFT representat…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
This paper presents a number of problems about mapping class groups and moduli space. The paper will appear in the book "Problems on Mapping Class Groups and Related Topics", ed. by B. Farb, Proc. Symp. Pure Math. series, Amer. Math. Soc.
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…
Thanks to the work of Karin Erdmann, we know a great deal about the representation theory of blocks of finite groups with tame representation type. Our purpose here is to examine the $p$-completed classifying spaces of these blocks and…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
The aim of this paper is to describe a large class of Hermitian Gray manifolds.
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…
This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major…
In the present paper, we propose a new construction of quantum Markov fields on arbitrary connected, infinite, locally finite graphs. The construction is based on a specific tessellation on the considered graph, that allows us to express…
We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space.…