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The Brauer–Manin obstruction provides a powerful framework for explaining failures of the Hasse principle for rational points on algebraic varieties. While many known examples arise from the algebraic part of the Brauer group, comparatively few...

For two multiplicatively independent positive integers p and q, Furstenberg (2019) conjectured that the transformations px mod 1 and qx mod1 are transverse. This means that the Hausdorff dimension of the intersection of two closed invariant sets is...

Since its inception in the early 2000s, compressive sensing has become a well-established paradigm for efficient signal recovery, with applications ranging from medical imaging to scientific computing. More recently, data-driven reconstruction...

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...

Stoichiometric principles provide a rigorous, law-based backbone for building mechanistic models that are robust and empirically testable through conservation and physiological constraints. In this talk, I will introduce stoichiometric models that...

Abstract TBA

Abstract TBA

Abstract TBA

I will tell the story of a mathematical problem which can be understood and tested by a child, yet which has resisted solution for over a century, in spite of the efforts of many prominent mathematicians. I will describe in parallel the development...

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...