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Let C be a class of algebraic structures. For example, C could be a class of quadratic forms, field extensions or algebraic curves of a given genus. To measure the complexity of C, mathematicians ask a natural question: how many algebraically...

A c-colouring of a combinatorial design is an assignment of colours, chosen from a set of size c, to the points of the design. A c-colouring is equitable if every block of size k contains ⌊k/c⌋ or ⌈k/c⌉ points of each colour. In 2016, Luther and Pike...

One of my favorite quotations in mathematics is due to Titchmarsh, who remarked: “The finer theory of the partial sums of the Möbius function is extremely obscure, and the results are not nearly so precise as the corresponding ones in the prime...