相关论文: Computational Geometry Column 37
The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a…
An expository description of smooth cubic curves in the real or complex projective plane.
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in…
In this paper we review nine previous proposed and solved problems of elementary 2D geometry, and we extend them either from triangles to polygons or polyhedrons, or from circles to spheres (from 2D-space to 3D-space) and make some…
This volume contains the proceedings of DCM 2023, the 13th International Workshop on Developments in Computational Models held on 2 July 2023 in Rome, Italy. DCM 2023 was organised as a one-day satellite event of FSCD 2023, the 8th…
This volume contains the post-proceedings of the Sixteenth International Workshop on Graph Computation Models (GCM 2025). The workshops took place in Koblenz, Germany on June 10 as part of STAF (Software Technologies: Applications and…
We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a…
We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as…
This paper studies the C-compact-open topology on the set C(X) of all realvalued continuous functions on a Tychonov space X and compares this topology with several well-known and lesser known topologies. We investigate the properties…
This is a collection of open problems and research ideas following the presentations and the discussions of the AGATES Kickoff Workshop held at the Institute of Mathematics of the Polish Academy of Sciences (IMPAN) and at the Department of…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Lecture notes of an algebraic geometry graduate course. The topics covered are as follows. Cohomology: ext sheaves and groups, cohomology with support, local cohomology, local duality. Duality: relative duality, Cohen-Macaulay schemes.…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
It will be shown that the polynomial time computable numbers form a field, and especially an algebraically closed field.