相关论文: Computational Geometry Column 34

Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…

Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…

We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…

These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…

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…

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…

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

In this note, we propose some open problems and questions about bounded convex domains in $\mathbb C^N$, specifically about visibility and iteration theory.

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…

These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

DCM 2010 provides a forum for ideas about new computing means and models, with a particular emphasis in 2010 on computational and causal models related to physics and biology. We believe that bringing together different approaches - in a…

Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries,…

In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…

We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description…

$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…

The conference Unexpected Phenomena in Energy Minimization and Polarization, held in Sofia, Bulgaria in 2024, provided a platform for researchers to discuss and propose challenging open questions across various fields, such as potential…

The proof of Dey's new k-set bound is illustrated.

This is the 34th issue of this bulletin, dedicated to selection principles in mathematics. Announcements include, among other things, a call for papers for the Topology and its Applications special issue on selection principles, and the…