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SUMMARY:Integral points of bounded height via universal torsors
DTSTART:20191128T151500
DTEND:20191128T164500
DTSTAMP:20260528T030931Z
UID:5932dce8f51ec998ef62a46363bf773eaf0e7ab0e2621ddbdf79060a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Florian Wilsch (IST Austria)\nA conjecture of Manin’s relate
 s the number of rational points of bounded height on Fano varieties with t
 heir geometric properties. Analogously to this conjecture on rational poin
 ts\, we study the distribution of integral points of bounded height. To do
  so\, we parametrize integral points using universal torsors\, and use ana
 lytic techniques to count integral points on the torsor – a method used 
 previously to count rational points.\n\nA result on a toric variety contra
 dicts parts of a preprint by Chambert-Loir and Tschinkel. Morally\, this i
 s explained by an obstruction to the existence of integral points on a cer
 tain region of the variety that should have dominated the total number. We
  describe this obstruction and its relation with the geometric interpretat
 ion of asymptotic formulas for the number of integral points of bounded he
 ight.
LOCATION:GR C0 01 https://plan.epfl.ch/?room==GR%20C0%2001
STATUS:CONFIRMED
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