Surveys in Combinatorics 2015

This volume contains nine survey articles based on the invited lectures given at the 25th British Combinatorial Conference, held at the University of Warwick in July 2015. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, Ramsey theory, combinatorial geometry and curves over finite fields. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.Preface Artur Czumaj, Agelos Georgakopolous, Daniel Kral', Vadim Lozin and Oleg Pikhurko; 1. Ramsey classes: examples and constructions Manuel Bodirsky; 2. Recent developments in graph Ramsey theory David Conlon, Jacob Fox and Benny Sudakov; 3. Controllability and matchings in random bipartite graphs Paul Balister and Stefanie Gerke; 4. Some old and new problems in combinatorial geometry I: around Borsuk's problem Gil Kalai; 5. Randomly generated groups Tomasz Luczak; 6. Curves over finite fields and linear recurring sequences Omran Ahmadi and Gary McGuire; 7. New tools and results in graph minor structure theory Sergey Norin; 8. Well quasi-order in combinatorics: embeddings and homomorphisms Sophie Huczynska and Nik Ruskuc; 9. Constructions of block codes from algebraic curves over finite fields Liming Ma and Chaoping Xing.