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SUMMARY:Knots\, $q$-series\, and modular forms [MPIM]
DTSTART:20260513T123000Z
DTEND:20260513T133000Z
DTSTAMP:20260716T202300Z
UID:indico-event-1290@math-events.uni-bonn.de
DESCRIPTION:Speakers: Matthias Storzer (UC Cork)\n\nNumber theory lunch se
 minar\nTo study knots\, invariants like the colored Jones polynomials (CJP
 ) are used. For alternating knots\, it is known that the coefficients of t
 he CJP stabilize and thus\, they converge to a well-defined $q$-series\, t
 he tail of the CJP. For several but not all knots with up to 10 crossings\
 , the tail of the CJP can be written as a product of (partial) theta funct
 ions and thus has modular properties. In this talk\, we present a general 
 formula for a class of knots\, and argue that the tail of the CJP for othe
 r knots does not have any modular properties. We will also discuss a poten
 tial connection to exceptional hyperbolic surgery on knots.\nThis talk is 
 based on joint work with Robert Osburn (Cork).\n\nhttps://math-events.uni-
 bonn.de/event/1290/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1290/
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