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SUMMARY:Knots\, $q$-series\, and modular forms [MPIM]
DTSTART:20260513T123000Z
DTEND:20260513T133000Z
DTSTAMP:20260508T062600Z
UID:indico-event-1290@math-events.uni-bonn.de
DESCRIPTION:Speakers: Matthias Storzer (UC Cork)\n\nNumber theory lunch se
 minar\no study knots\, invariants like the colored Jones polynomials (CJP)
  are used. For alternating knots\, it is known that the coefficients of th
 e CJP stabilize and thus\, they converge to a well-defined $q$-series\, th
 e 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 functi
 ons and thus has modular properties. In this talk\, we present a general f
 ormula for a class of knots\, and argue that the tail of the CJP for other
  knots does not have any modular properties. We will also discuss a potent
 ial connection to exceptional hyperbolic surgery on knots.\nThis talk is b
 ased on joint work with Robert Osburn (Cork).\n\nhttps://math-events.uni-b
 onn.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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