Oct 3

Title: Bonahon-Wong-Yang volume conjecture for incomplete structures

Speaker: Tushar Pandey (Texas A&M university)

Abstract: In 2021, F. Bonahon, H. Wong, and T. Yang defined quantum invariants for self-homeomorphisms of a surface using the representation theory of Kauffman Bracket Skein algebra. They conjectured that the invariants capture the hyperbolic volume of the mapping torus corresponding to the complete hyperbolic structure. They verified the conjecture numerically for some cases and proved it for the one-puncture torus bundles. Together with Ka Ho Wong, we extend this conjecture such that the quantum invariants constructed above also capture the volume of cone manifolds when the manifolds are mapping tori. We also provide some recent developments and results for both the conjectures.