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Daily Overview |
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AG1: Algebraic Geometry Location: A701 Session Chair: Mateusz Michalek Session Chair: Botong Wang | |
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Representation theory over bands 1: Brown University, United States; 2: Durham University, United Kingdom This talk presents an overview of ongoing research into representation theory over bands, which are combinatorial generalisations of fields, with applications in matroid theory and tropical geometry. A fundamental departure from the classical theory arises from the observation that natural general linear objects in this setting cannot carry group structure; they are instead monoids. To construct a general linear monoid, we study the multiplication of bimatroids and matrices over bands, investigate their interrelations, and construct their moduli spaces as combinatorial analogues of the determinantal variety. These constructions provide the foundation for defining band analogues of classical matrix groups and their representations. As a proof of concept, we conclude with a study of Schur functors in this new setting. | |
