Surveys in Combinatorics 2021
London Mathematical Society Lecture Note Series

This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse?Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.

1. The partition complex: an invitation to combinatorial commutative algebra Karim Adiprasito and Geva Yashfe; 2. Hasse-Weil type theorems and relevant classes of polynomial functions Daniele Bartoli; 3. Decomposing the edges of a graph into simpler structures Marthe Bonamy; 4. Generating graphs randomly Catherine Greenhill; 5. Recent advances on the graph isomorphism problem Martin Grohe and Daniel Neuen; 6. Extremal aspects of graph and hypergraph decomposition problems Stefan Glock, Daniela Kühn and Deryk Osthus; 7. Borel combinatorics of locally finite graphs Oleg Pikhurko; 8. Codes and designs in Johnson graphs with high symmetry Cheryl E. Praeger; 9. Maximal subgroups of finite simple groups: classifications and applications Colva M. Roney-Dougal.

Konrad K. Dabrowski is Teaching Fellow in the Department of Computer Science at Durham University.
Maximilien Gadouleau is Associate Professor in the Department of Computer Science at Durham University.
Nicholas Georgiou is Assistant Professor in the Department of Mathematical Sciences at Durham University.
Matthew Johnson is Professor in the Department of Computer Science at Durham University.
George B. Mertzios is Associate Professor in the Department of Computer Science at Durham University.
Daniël Paulusma is Professor in the Department of Computer Science at Durham University.