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SUMMARY:Toshiki Matsusaka (Nagoya University)
DTSTART:20201110T084000Z
DTEND:20201110T091000Z
DTSTAMP:20260423T010922Z
UID:JENTE/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/10/">L
 inking numbers and modular forms for the triangle groups</a>\nby Toshiki M
 atsusaka (Nagoya University) as part of Japan Europe Number Theory Exchang
 e Seminar\n\n\nAbstract\nThe coset space SL(2\,Z)\\SL(2\,R) is diffeomorph
 ic to the complement of the trefoil knot in the 3-sphere. For each hyperbo
 lic matrix in SL(2\,Z) or real quadratic irrationality\, we can naturally 
 construct a simple closed orbit in this space\, which is called a modular 
 knot. At ICM 2006\, Ghys showed a beautiful relation that the linking numb
 er of the modular knot and the missing trefoil is equal to the Rademacher 
 invariant. This invariant classically appears in the transformation law of
  the Dedekind eta function\, and has the expression as a geodesic cycle in
 tegral of the Eisenstein series of weight 2. In this talk\, we generalize 
 Ghys’ result to the knot complement of the torus knots. To get a similar
  relation between linking numbers and cycle integrals\, modular forms for 
 triangle groups have crucial roles. This is joint work with Jun Ueki (Toky
 o Denki University).\n
LOCATION:https://researchseminars.org/talk/JENTE/10/
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