Courses in Discrete and Computational Geometry (Bolyai Society Mathematical Studies)

Pach, János (EDT)/ Tóth, Géza (EDT)

Springer Nature Switzerland AG（2026/01発売）

• 製本 Hardcover:ハードカバー版
• 言語 ENG
• 商品コード 9783032105028

Full Description

In the Fall of 2023, the Erdős Center (Budapest) hosted a special semester on "Discrete Geometry and Convexity", which brought together some of the strongest experts in the field and many outstanding young researchers. The program featured intensive one-week mini-courses during a summer school, followed by conferences and workshops presenting cutting-edge research. Part I of the present volume includes the notes of three lecture series on: (1) approximation in discrete geometry, (2) on random polytopes, and (3) on a structure theory for graphs embedded in the plane. Part II starts with a classic: Matoušek's until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects. It is complemented by the first systematic and comprehensive survey of the corresponding complexity class: the existential theory of reals. This volume will be a valuable resource for graduate students, young researchers, and experts in related fields interested in discrete and computational geometry.

Contents

Part I. Lecture notes.- Chapter 1. Graph Product Structure Theory with Applications.- Chapter 2. Threshold for the measure of random polytopes.- Chapter 3. Approximation in geometry.- Part II. The Existential Theory of the Reals.- Chapter 4. Intersection graphs of segments and ∃R.- Chapter 5. The Existential Theory of the Reals as a Complexity Class: A
Compendium.