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DTSTART:19810329T020000
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UID:news2041@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260526T090344
DTSTART;TZID=Europe/Zurich:20260527T101500
SUMMARY:Number Theory Seminar: Vesselin Dimitrov (Caltech)
DESCRIPTION:Title: Arithmetic holonomy bounds in transcendence proofs and e
 ffective Diophantine approximation.\\r\\nAbstract: The method of arithmeti
 c holonomy bounds\, developed presently in a collaboration with Calegari a
 nd Tang\, encodes some Diophantine problems of a traditional interest into
  suitable generating functions with good analytic and Diophantine properti
 es. I will present a completely explicit Ansatz and explain its fairly str
 aightforward proof. The challenge is then to cook up holonomy template set
 ups where the Ansatz has interesting consequences. Nevertheless\, already 
 the simplest “infinite dihedral orbifold” setup has applications inclu
 ding the transcendence of Pi (in a particularly simple way) and a new effe
 ctive solution of the two-variable S-unit equation\, but also some explici
 t irrationality measures for logarithms that seem to enter into a blind sp
 ot of the literature.\\r\\nNew room: Seminarraum 00.002\, Rheinsprung 21
X-ALT-DESC:<h2>Title: Arithmetic holonomy bounds in transcendence proofs an
 d effective Diophantine approximation.</h2>\n<p><br />Abstract: The method
  of arithmetic holonomy bounds\, developed presently in a collaboration wi
 th Calegari and Tang\, encodes some Diophantine problems of a traditional 
 interest into suitable generating functions with good analytic and Diophan
 tine properties. I will present a completely explicit Ansatz and explain i
 ts fairly straightforward proof. The challenge is then to cook up holonomy
  template setups where the Ansatz has interesting consequences. Neverthele
 ss\, already the simplest “infinite dihedral orbifold” setup has appli
 cations including the transcendence of Pi (in a particularly simple way) a
 nd a new effective solution of the two-variable S-unit equation\, but also
  some explicit irrationality measures for logarithms that seem to enter in
 to a blind spot of the literature.</p>\n<p><strong>New room: Seminarraum 0
 0.002\, Rheinsprung 21</strong></p>
DTEND;TZID=Europe/Zurich:20260527T111500
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