Fathi Ben Aribi - FAMED triangulations and volume conjectures - IPAM at UCLA
Recorded 12 October 2026. Fathi Ben Aribi of the Institut de Mathématiques de Jussieu - Paris Rive Gauche presents "FAMED triangulations and volume conjectures" at IPAM's Hyperbolic Structures and Quantum Invariants Workshop.Worksheet: https://www.normalesup.org/~benaribi/Printout_FAMED.pdf
Abstract: A volume conjecture relates a certain asymptotical growth of a given quantum topological invariant of a hyperbolic 3-manifold to the hyperbolic volume of this manifold.
In this talk I will mention several of these volume conjectures, their common points and differences, notably those associated to the Baseilhac-Benedetti invariants and to the Andersen-Kashaev TQFT.
A general strategy to prove a volume conjecture is to use the combinatorial properties of a given triangulation of the manifold to simplify the expression of the quantum invariant, and hopefully to successfully apply the saddle point method in the desired asymptotics. The FAMED property for triangulations has such potential, as it helped us prove the Andersen-Kashaev volume conjecture for triangulations of the first 42000 knots.
I will use the figure-eight knot complement as a recurring example, as it is the simplest member of two infinite families, the hyperbolic twist knots and the once-punctured torus bundles over the circle.
No prerequisite in quantum topology or hyperbolic geometry will be needed.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-hyperbolic-structures-and-quantum-invariants/?tab=overview Receive SMS online on sms24.me
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