Surveys in Combinatorics 2019
London Mathematical Society Lecture Note Series

This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. 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, cryptography, matroids, incidence geometries and graph limits. 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.

1. Clique-width for hereditary graph classes Konrad K. Dabrowski, Matthew Johnson and Daniёl Paulusma; 2. Analytic representations of large graphs Andrzej Grzesik and Daniel Král; 3. Topological connectedness and independent sets in graphs Penny Haxell; 4. Expanders – how to find them, and what to find in them Michael Krivelevich; 5. Supersingular isogeny graphs in cryptography Kristin E. Lauter and Christophe Petit; 6. Delta-matroids for graph theorists Iain Moffatt; 7. Extremal theory of vertex or edge ordered graphs Gábor Tardos; 8. Some combinatorial and geometric constructions of spherical buildings Hendrik Van Maldeghem and Magali Victoor.

Allan Lo is Lecturer in Mathematics at the University of Birmingham.
Richard Mycroft is Senior Lecturer in Mathematics at the University of Birmingham.
Guillem Perarnau is a lecturer at Universitat Politècnica de Catalunya, Barcelona.
Andrew Treglown is Senior Lecturer in Mathematics at the University of Birmingham.