Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Modular Knots, Automorphic Forms, and the Rademacher Symbols for Triangle Groups
Toshiki Matsusaka (Nagoya University)
Abstract:
In a celebrated paper “Knots and dynamics”, Étienne Ghys proved that the linking numbers of modular knots and the missing trefoil in
coincide with the values of a highly ubiquitous function called the Rademacher symbol for
. In this talk, we replace
by the triangle group
for any coprime pair $(p,q)$ of integers with
. We invoke the theory of harmonic Maass forms for
to introduce the notion of the Rademacher symbol and provide several characterizations. Among other things, we generalize Ghys’s theorem for modular knots around any missing torus knot in
and in a lens space. This is joint work with Jun Ueki (Tokyo Denki University).
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