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Full Description
This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, held at Queen Mary University of London in July 2024. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include: Latin squares, Erdős covering systems, finite field models, sublinear expanders, cluster expansion, the slice rank polynomial method, and oriented trees and paths in digraphs. The authors are among the world's foremost researchers on their respective topics but their surveys are accessible to nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, helping researchers and graduate students in mathematics and theoretical computer science to keep abreast of the latest developments in the field.
Contents
1. Intersection theory of matroids: variations on a theme Federico Ardila-Mantilla; 2. Erdős covering systems Paul Balister; 3. The cluster expansion in combinatorics Matthew Jenssen; 4. Sublinear expanders and their applications Shoham Letzter; 5. Transversals in Latin squares Richard Montgomery; 6. Finite field models in arithmetic combinatorics - twenty years on Sarah Peluse; 7. The slice rank polynomial method - a survey a few years later Lisa Sauermann; 8. An introduction to transshipments over time Martin Skutella; 9. Oriented trees and paths in digraphs Maya Stein.
