Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  math 
Date  Monday 9 October 2023 
Time  16:00 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  Marché 
Speaker's First Name  Julien 
Speaker's Email Address  
Speaker's Institution  IMJPRG 
Title  Signatures of Quantum Representations and 2bridge Knots 
Abstract  Quantum representations are families of finitedimensional representations of mapping class groups satisfying strong compatibility conditions. One of the most wellknown (the socalled SO(3)TQFT) depends on a parameter q which is a root of unity of order 2r (r odd). These representations preserve a Hermitian form: recently, with B. Deroin, we explained how to compute its signature (among other things). More recently, I observed that this computation is related to the trace field of the 2bridge knot K(r,s) where q=exp(iπs/r). During the talk, I will explain this relation and the objects involved in it. 
arXiv Preprint Number  
Comments  Séminaire Géométrie et groupes discrets 
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