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Globus Seminar
September 28, 2017 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)
 


Units, K-theory, and quantum invariants of knots

D. Zagier

Max Planck Institute for Mathematics
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D. Zagier


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Abstract: In recent years, there has been intense interest in the quantum invariants of knots and their asymptotic properties, a typical example being the celebrated Volume Conjecture for the Kashaev invariant. But it turns out there are also very interesting arithmetic properties of these invariants, including a surprising near-modular transformation property. Even though many of these are only conjectural, one can check them numerically to high precision, and when one does this, algebraic numbers of a special sort (roots of units in certain number fields) appear by magic. This led, in joint work with Frank Calegari and Stavros Garoufalidis, to a new (non-conjectural) construction of units starting from elements in so-called Bloch groups, and as a side product also to a solution of Nahm's conjecture on the modularity of certain special q-hypergeometric series.

Language: English

Website: http://ium.mccme.ru/GLOBUSabstracts/Globus_Zagier.pdf

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