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Mahler measure and the Vol-Det Conjecture

Banff International Research Station for Mathematical Innovation and Discovery

For a hyperbolic link in the 3-sphere, the hyperbolic volume of its complement is an interesting and well-studied geometric link invariant. Similarly, the determinant of a link is one of the oldest diagrammatic link invariant. In previous work we studied the asymptotic behavior of volume and determinant densities for alternating links, which led us to conjecture a surprisingly simple relationship between the volume and determinant of an alternating link, called the Vol-Det Conjecture. In this talk we outline an interesting method to prove the Vol-Det Conjecture for infinite families of alternating links using a variety of techniques from the theory of dimer models, Mahler measures of 2-variable polynomials and the hyperbolic geometry of link complements in the thickened torus.

Mathematics; Number theory; Manifolds and cell complexes

video/mp4

Author affiliation: College of Staten Island & The Graduate Center, CUNY

2018-09-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67133

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/