Textbook in PDF format

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.
Preface
The partition complex: an invitation to combinatorial commutative algebra
Hasse-Weil type theorems and relevant classes of polynomial functions
Decomposing the edges of a graph into simpler structures
Generating graphs randomly
Recent advances on the graph isomorphism problem
Extremal aspects of graph and hypergraph decomposition problems
Borel combinatorics of locally finite graphs
Codes and designs in Johnson graphs with high symmetry
Maximal subgroups of finite simple groups: classifications and applications