Related papers: Ruled surface theory and incidence geometry

This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…

This manuscript collects three independent works: arXiv:1902.03805, arXiv:1906.04444, with Antonio Lerario and arXiv:2103.10853, together with some additional results, observations, examples and comments, some of which were taken up in the…

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…

A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.

These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.

The aim of this book is to provide an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the `70s. The book covers many aspects of Penrose tilings, including the…

The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.

This note provides an overview of the notion of observable within the setting of multisymplectic geometry. We essentially follow the ideas described by F. H\'elein and J. Kouneiher [17] [18] [19] and in particular in keeping with the…

In this paper, we study the embedded topology of smooth plane quartics and its bitangent lines via two-graphs and apply it to construct interesting examples for Zariski $m$-ple.

The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…

We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we show that our Randers surface of revolution can be embedded in…

The present work constitutes the third installment in a series of investigations devoted to discrete conformal structures on surfaces with boundary. In our preceding works \cite{X-Z DCS1, X-Z DCS2}, we established, respectively, a…

This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…

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…

We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two…

In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.