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SUMMARY:Applications of lunacy to finding small solutions of two variable 
 congruences
DTSTART:20260528T150000Z
DTEND:20260528T160000Z
DTSTAMP:20260524T181100Z
UID:indico-event-16537@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ted Chinburg (University of Pennsylvania)\n\nIn 2000
 \, Boneh and Durfee showed that if a certain heuristic hypothesis is true\
 , one can find all small solutions of certain two variable congruences usi
 ng the LLL algorithm for finding small non-zero elements of lattices.   T
 he truth of the heuristic hypothesis has been an open question since 2000\
 , however.  In this talk I will discuss how one can use capacity theory o
 n curves to show that the heuristic hypothesis actually fails in a positiv
 e proportion of cases\, and that it also holds in a positive proportion of
  cases.  One step in the proof involves the potential theory of regions i
 n the complex plane that are the complement in a large closed disk of a sm
 aller open disk.  Such regions are called lunes because they look like a 
 waxing or waning moon.  This is joint work with Stephen Miller. \n\nhttp
 s://indico.math.cnrs.fr/event/16537/
LOCATION:Salle Pellos (1R2)
URL:https://indico.math.cnrs.fr/event/16537/
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