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Owen Rouillé

Computation of 3-manifold invariants
Vendredi, 11 Mars, 2022 - 10:30
Résumé : 

Intuition is very important in research, but can be difficult to get on complex objects. The task can even be daunting when new instances are hard to compute. This presentation describes the computation of two objects on 3-manifolds revolving around the hyperbolic volume: the invariants of Turaev-Viro and the complete hyperbolic structures.
The invariants of Turaev-Viro are a family of quantum invariants indexed by an integer. They are difficult (#P hard) to compute, but are efficient at distinguishing manifolds and they are at the center of a conjecture similar to the volume conjecture about the Jones polynomials. We look at their computation and their behavior for a census of manifolds.
The complete hyperbolic structures are solutions to Thurston's gluing equations, they link topology and geometry of cusped hyperbolic manifolds. We propose a method to compute these based on an approach from Casson and Rivin.

Institution de l'orateur : 
INRIA Université Côte d'Azur
Thème de recherche : 
Salle : 
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