Related papers: The Kempf-Ness theorem and Invariant Theory
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
The aim of this paper is to describe an approach to a a strengthened form of J. Tits' Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G. R. Kempf from Geometric Invariant Theory and…
In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of…
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.
We explore a family of invariants obtained from linking numbers. This is a family of Kauffman finite type invariants.
We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss examples which are "ft-independent" and examples which are…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.
We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the…
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce…
In this paper we introduce a group invariant version of the wellknown Ekeland variational principle. To achieve this, we defne the concept of convexity with respect to a group and establish a version of the theorem within this framework.…
We prove some fundamental results like localization, excision, Nisnevich descent and the Mayer-Vietoris property for equivariant regular blow-up for the equivariant K-theory of schemes with an affine group scheme action. We also show that…
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.
We prove existence of an invariant measure on a hypergroup.