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UID:6707@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200707T110000
DTEND;TZID=Europe/Paris:20200707T120000
DTSTAMP:20241120T201943Z
URL:https://www.i2m.univ-amu.fr/evenements/quantum-modular-forms-trigonome
 tric-products-and-quadratic-irrationals/
SUMMARY:Bence Borda (TU Graz): Quantum modular forms\, trigonometric produc
 ts and quadratic irrationals
DESCRIPTION:Bence Borda: WEBINAIRE (lien: https://webconf.lal.cloud.math.cn
 rs.fr/b/pie-hmu-en9)\nRésumé : Quantum invariants of hyperbolic knots ha
 ve rich arithmetic structure. In this talk we consider an extension to the
  rationals of the so-called  Kashaev invariant of the figure eight knot\,
  a quantum modular form in  the sense of Zagier. We find its asymptotics 
 along the sequence of best  rational approximations to a given quadratic 
 irrational\, and show that  this asymptotics deviates from that of well a
 pproximable irrationals  recently established by Bettin and Drappeau. Our
  proof exploits the  close connection between the Kashaev invariant and S
 udler's  trigonometric product\; in particular\, we use a recent result o
 f  Grepstad\, Neumuller and Zafeiropoulos on the convergence of certain 
  normalized and shifted versions of Sudler's products at quadratic irratio
 nals.\nJoint work with Christoph Aistleitner.\nBence Borda (TU Graz)
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/07/Bence_Borda.jpg
CATEGORIES:Séminaire,Ernest,Virtual event
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
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 e de Séminaire 304-306 (3ème étage):geo:0,0
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