Graph Theory and Additive Combinatorics

Exploring Structure and Randomness
Erscheinungsjahr 2023
ISBN: 978-1-009-31094-9
Verlag: Cambridge University Press

Buch, Englisch, 338 Seiten, Format (B × H): 183 mm x 254 mm, Gewicht: 768 g

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

Autoren/Hrsg.

Zhao, Yufei

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Preface; Notation and Conventions; Appetizer: triangles and equations; 1. Forbidding a subgraph; 2. Graph regularity method; 3. Pseudorandom graphs; 4. Graph limits; 5. Graph homomorphism inequalities; 6. Forbidding 3-term arithmetic progressions; 7. Structure of set addition; 8. Sum-product problem; 9. Progressions in sparse pseudorandom sets; References; Index.

Über Autor(innen)

Zhao, Yufei
Yufei Zhao is Associate Professor of Mathematics at the Massachusetts Institute of Technology. His research tackles a broad range of problems in discrete mathematics, including extremal, probabilistic, and additive combinatorics, graph theory, and discrete geometry, as well as applications to computer science. His honors include the SIAM Dénes Konig prize (2018), the Sloan Research Fellowship (2019), and the NSF CAREER Award (2021). This book is based on an MIT graduate course, which he has taught and developed over the last five years.