Surveys in Combinatorics 2013
London Mathematical Society Lecture Note Series

This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. 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, matroid theory and automatic counting, as well as connections to coding theory and Bent functions. 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; 1. Graph removal lemmas David Conlon and Jacob Fox; 2. The geometry of covering codes: small complete caps and saturating sets in Galois spaces Massimo Giulietti; 3. Bent functions and their connections to combinatorics Tor Helleseth and Alexander Kholosha; 4. The complexity of change Jan van den Heuvel; 5. How symmetric can maps on surfaces be? Jozef Širáň; 6. Some open problems on permutation patterns Einar Steingrímsson; 7. The world of hereditary graph classes viewed through Truemper configurations Kristina Vušković; 8. Structure in minor-closed classes of matroids Jim Geelen, Bert Gerards and Geoff Whittle; 9. Automatic counting of tilings of skinny plane regions Shalosh B. Ekhad and Doron Zeilberger.

Simon R. Blackburn studied in Bristol and Oxford, following which he rose through the ranks at Royal Holloway, initially as a Research Assistant and EPSRC Advanced Fellow (working on various aspects of cryptography) and then as a Reader and Professor. He is a member of the BSHM, IACR, IEEE and LMS, an associate member of the AMS, and a Fellow of the ICA and IMA. His research involves combinatorics, cryptography, communication theory, algebra and the connections between them.
Stefanie Gerke studied at the FU Berlin and the University of Oxford before moving on to work at the TU Munich, the ETH Zurich and now Royal Holloway, University of London. She is a member of the DMV, LMS and HEA and has won several awards for her research and innovative teaching. She works mainly in probabilistic graph theory and algorithms.
Mark Wildon studied in Cambridge and Oxford, after which he worked in Oxford as a College Lecturer and Bristol as a Research Fellow, before joining Royal Holloway, University of London in 2010. He is a member of the AMS and LMS. He is the co-author of a highly praised textbook on Lie algebras and in 2012 was awarded a university prize for teaching excellence. His main research interests are combinatorics and representation theory, especially the representation theory of the symmetric group.