Related papers: Towards a Model Theory for Transseries
We formalise the teleparallel version of extended geometry (including gravity) by the introduction of a complex, the differential of which provides the linearised dynamics. The main point is the natural replacement of the two-derivative…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
We present some open problems and describe briefly some possible research directions in the emerging theory of Hardy spaces of Dirichlet series and their intimate counterparts, Hardy spaces on the infinite-dimensional torus. Links to number…
In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$…
We study model transition for representations occurring in the local theta correspondence between split even special orthogonal groups and symplectic groups, over a non-archimedean local field of characteristic zero.
We give examples of $\mathrm{NIP}$ structures in which new algebraic structure appears in the Shelah completion. In particular we construct a weakly o-minimal structure $\mathscr{M}$ such that $\mathscr{M}$ does not interpret an infinite…
It is important in many applications to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of the paper is to provide an elementary…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
We present two different aspects of the anomalies in quantum field theory. One is the dispersion relation aspect, the other is differential geometry where we derive the Stora--Zumino chain of descent equations.
We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does not satisfy any of the combinatorial tameness properties…
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of…
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
We develop a model-independent approach to lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a…