Related papers: A Note on Twistor Integrals
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found.…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
In this article, we present semiorthogonal decompositions for twisted forms of grassmannians
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
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…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
This article is based on the lectures in the Winter Braids V (Pau, Feb. 2015). Main puposel of this is to explain how to compute twisted Alexander polynomials for non-experts.
We review the twistorial structures by providing a setting under which the corresponding (differential) geometry can be described, by involving the $\rho$-connections. This applies, for example, to give new proofs of the existence of the…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
An expository description of smooth cubic curves in the real or complex projective plane.
We explain what Cartan geometries are, aiming at an audience of graduate students familiar with manifolds, Lie groups and differential forms.