Courses in Discrete and Computational Geometry
Buch in deiner Nähe kaufen
Beschreibung
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 Part II starts with a classic: Matoušek’s until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects.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.
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 Part II starts with a classic: Matoušek’s until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects.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.
Includes the material from 4 intensive mini-courses on hot topics in discrete geometry Provides the first systematic survey of the existential theory of reals Illustrates the interplay between combinatorial, geometric, and topological methods
Autor*in
János Pach
Themen in »Courses in Discrete and Computational Geometry«
Graph embeddings Structural graph theory Treewidth Tukey half-space depth Log-concave probability measure Cramér transform VC-dimension Quantitative Helly theorem Epsilon-nets Intersection graphs Existential theory of reals Stretchability Computational complexity