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SUMMARY:Asymptotic Mahler measure of Gaussian periods [MPIM]
DTSTART:20250612T130000Z
DTEND:20250612T140000Z
DTSTAMP:20260415T093100Z
UID:indico-event-482@math-events.uni-bonn.de
DESCRIPTION:Speakers: Gunther Cornelissen (Universiteit Utrecht/MPIM)\n\nM
 PI-Oberseminar\nI will describe a construction of a family of algebraic in
 tegers (Gaussian periods) with cyclic Galois group and small Mahler measur
 e/height. Studying their asymptotics as a function of the degree (essentia
 lly a problem of Quasi-Monte-Carlo integration) leads to a family of Calab
 i-Yau varieties constructed from reflexive polytopes\, whose Mahler measur
 e in turn can be studied via probability theory (similar to the computatio
 n of density of states in graphite) as their dimension grows. Finally\, we
  run into a problem related to the smallest prime in an arithmetic progres
 sion. Computations indicate interesting growth behaviour (better than the 
 currently proven non-zero constant) of the smallest height of a non-cyclot
 omic integer with cyclic Galois group\, as a function of its degree. \nAll
  notions will be defined and a lot of examples will be given. (Joint work 
 with David Hokken and Berend Ringeling.) \n \n\nhttps://math-events.uni-b
 onn.de/event/482/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/482/
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