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UID:20251007T054617EDT-1189hSTsfn@132.216.98.100
DTSTAMP:20251007T094617Z
DESCRIPTION:Topological Explosion and Supercancellation in Arithmetic Stati
 stics\n\n \n\nAbstract:\n\n \n\nThe fundamental question (*) How many solu
 tions does a system of polynomial equations have modulo a fixed prime numb
 er p?  drives the burgeoning field of arithmetic statistics. \n\nUnderstan
 ding the statistical behavior of the number of solutions within families o
 f algebraic varieties of increasing complexity is subtle due to 'topologic
 al explosion'.  We will describe several interesting families exhibiting t
 opological explosion and the 'supercancellation' necessary for proving tha
 t the statistics of (*) are captured by reasonable heuristic models.  \n\n
 We will also discuss joint work with Jacob Tsimerman on the failure of sup
 ercancellation for abelian varieties of large dimension over finite fields
 .  This failure results in some statistically counterintuitive behavior.  
 For example\, most principally polarized abelian varieties of large dimens
 ion over a fixed finite field are essentially powers of elliptic curves an
 d do not obey Cohen-Lenstra heuristics. \n
DTSTART:20161216T210000Z
DTEND:20161216T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Michael Lipnowski University of Toronto
URL:/mathstat/channels/event/michael-lipnowski-univers
 ity-toronto-264756
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