Status  Confirmed 
Seminar Series  SEMDARBOUX 
Subjects  math.QA 
Date  Thursday 18 January 2024 
Time  11:00 
Institute  LPTHE 
Seminar Room  Library 
Speaker's Last Name  Brochier 
Speaker's First Name  Adrien 
Speaker's Email Address  
Speaker's Institution  IMJPRG (Grands Moulins) 
Title  Factorization homology of ribbon categories 
Abstract  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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