Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  math.QA 
Date  Jeudi 18 Janvier 2024 
Heure  11:00 
Institut  LPTHE 
Salle  Library 
Nom de l'orateur  Brochier 
Prenom de l'orateur  Adrien 
Addresse email de l'orateur  
Institution de l'orateur  IMJPRG (Grands Moulins) 
Titre  Factorization homology of ribbon categories 
Résumé  Ribbon categories are one of the fundamental example of the deep relation between lowdimensional topology, deformation quantization and quantum algebra: those arise naturally in representation theory, and lead to wellbehaved invariants of links and representations of braid groups. The formalism of factorization homology takes as input a ribbon category, and produces a categoryvalued invariant of oriented topological surfaces. This construction is in fact part of socalled 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. 
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