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Description
The János Bolyai Mathematical Society and the HUN-REN Alfréd Rényi Institute of Mathematics (Budapest, Hungary) organized a week-long conference on the occasion of the 70th birthdays of four excellent mathematicians: Péter Frankl, Zoltán Füredi, Ervin Györi and János Pach in July 2024. The present volume mainly contains survey papers written by the invited speakers of this conference and it also includes some interesting new results, see, for example, Noga Alon s paper in the area of extremal combinatorics. The book also comprises three excellent surveys written by Hurlbert, Kupavskii, and Jian Wang which give a good overview of extremal set theory. Moreover, two papers written by Balko and Verstraëte are surveys of certain sub-branches of Ramsey theory, while two papers written by Aslanyan-Sahakyan and Ihringer present a broad picture of the combinatorial properties of Boolean functions. Likewise, the paper written by Géza Tóth covers an interesting area of combinatorial geometry and in addition, there are subsequent papers presenting results on graph theory.
This volume will be a valuable resource for graduate students and young (perhaps also not so young) researchers interested in extremal combinatorics and combinatorial geometry.
Chapter 1. Some extremal problems of zero-sum theory in Additive Combinatorics.- Chapter 2. Problems and results in Extremal Combinatorics V.- Chapter 3. Monotone Boolean Reconstruction.- Chapter 4. A Survey on Ordered Ramsey Numbers.- Chapter 5. Structure and Noise in Dense and Sparse Random Graphs: Percolated Stochastic Block Model via the EM Algorithm and Belief Propagation with Non-Backtracking Spectra.- Chapter 6. Disjoint zero-sum subsets in Abelian groups and their application: A survey.- Chapter 7. A Stopping Game on Zero-Sum Sequences.- Chapter 8. Effective MC-finiteness.- Chapter 9. An overview of property B.- Chapter 10. A Survey of the Holroyd-Talbot Conjecture.- Chapter 11. A Survey of Cameron-Liebler Sets and Low Degree Boolean Functions in Grassmann Graphs.- Chapter 12. Results and Problems on Equitable Coloring of Graphs.- Chapter 13. Delta-system method: A survey.- Chapter 14. Recent advances in arrow relations and traces of sets.- Chapter 15. Transversal Structures in Graph Systems: A Survey.- Chapter 16. Generalizations of the Crossing Lemma.- Chapter 17. Recent Progress in Ramsey Theory.- Chapter 18. Developments of the shifting method in extremal set theory.
Gyula O.H. Katona is a research professor emeritus at HUN-REN Alfréd Rényi Institute of Mathematics and its former director as well. Gyula is an author of 170 research papers mostly in the area of extremal set theory and applications of combinatorics. Gyula is also a member of the editorial boards of 15 mathematical journals and a member of the Hungarian Academy of Sciences.
Balázs Patkós is a research professor at HUN-REN Alfréd Rényi Institute of Mathematics and an author of almost 100 research papers as well as a co-author of the book "Extremal Finite Set Theory". Balázs is also an associate editor of the journal Discrete Mathematics and Order.
Casey Tompkins is a researcher at HUN-REN Alfréd Rényi Institute of Mathematics and an author of more than 50 research articles. Casey is also the co-organizer of multiple seminars, conferences and workshops as well as an instructor at the Budapest Semesters in Mathematics program.
