Related papers: Course of differential geometry
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.
This is an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol. 2. After discussing (and proving) some of the fundamental results of contact topology (neighbourhood…
These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions,…
This is a short essay about some fundamental results on scalar curvature and the two key methods that are used to establish them.
The purpose of this thesis is to use the language of orbifold groupoids to describe the geometry and topology of orbifolds, highlighting advantages and disadvantages of this language as they arise.
In this paper, we study the differential smoothness of diffusion algebras.
These notes aim to give an introduction to a few aspects of noncommutative geometry.
Lectures notes in universal algebraic geometry for beginners
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an…
We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic…
This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
This is an intorduction to some of the basic methods and results of dense matter physics.It is aimed at readers interested in astrophysical and physical applications.
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…