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Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe…
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
There have been several attempts in recent years to extend the notions of symplectic and Poisson structures in order to create a suitable geometrical framework for classical field theories, trying to achieve a success similar to the use of…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a…
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…