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Résumé |
Ribbon categories are one of the fundamental example of the deep relation between low-dimensional topology, deformation quantization and quantum algebra: those arise naturally in representation theory, and lead to well-behaved invariants of links and representations of braid groups. The formalism of factorization homology takes as input a ribbon category, and produces a category-valued invariant of oriented topological surfaces. This construction is in fact part of so-called topological field theory, meaning that it is naturally compatible with the operations of cutting and gluing surfaces along (part of) their boundary. In this talk, I'll explain how those categories can be computed fairly explicitly and I'll present some applications: it provides, among other things, canonical quantizations of certain moduli spaces arising in mathematical physics, as well as an explicit description of certain mapping class and surface braid groups representations arising in conformal field theories. |
