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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...

Tensor triangular geometry associates a rich geometric structure, the spectrum, to a “nice” category where one can add, subtract and multiply objects. Examples include modules over a commutative ring and representations of a finite group. I’ll give...

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...

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...

Latent Dirichlet Allocation and Text embeddings have revolutionized the use of text as data leading to vastly improved document clustering and retrieval and recommender systems by finding lower dimensional structure in the text. Furthermore, these...

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