Related papers: A Note on Twistor Integrals
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.
Remarkably, the twistor $\mathbf P^1$ occurs as a fundamental object in both four-dimensional space-time geometry and in number theory. In Euclidean signature twistor theory it is how one describes space-time points. In recent work by…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
A general method for analytic inversion of geometric integral transforms is proposed
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set…
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven…
A short survey on applications of algebraic geometry in topological data analysis.
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
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…
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.
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
This is an expository paper in which we define projective GIT quotients and introduce toric varieties from this perspective. It is intended primarily for readers who are learning either invariant theory or toric geometry for the first time.
For the twistor spaces of the Bochner-K\"ahler manifold $M = H^l \times P^n$, systems of holomorphic coordinates are constructed. As an application of them, an explicit description of the moduli space of relative deformations of fibers of…
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these…
This is an attempt to look at the tropical geometry from topological point of view.