Courses in discrete and computational geometry János Pach, Géza Tóth, editors

Format:

Book

Author/Creator:

Pach, János

Contributor:

Pach, János, editor.

Tóth, Géza, editor.

Series:

Bolyai Society mathematical studies ; 2947-9460 31

Bolyai Society Mathematical Studies 2947-9460 volume 31

Language:

English

Subjects (All):

Discrete geometry.

Convex geometry.

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2026

Summary:

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) random polytopes, and (3) 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 Part II starts with a classic: Matoušek's until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects.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

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed May 28, 2026)

ISBN:

9783032105035

303210503X

OCLC:

1593088714

Access Restriction:

Restricted for use by site license