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SUMMARY:Alexander Smith (Stanford)
DTSTART:20221122T213000Z
DTEND:20221122T223000Z
DTSTAMP:20260423T125940Z
UID:MITNT/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/63/">S
 imple abelian varieties over finite fields with extreme point counts</a>\n
 by Alexander Smith (Stanford) as part of MIT number theory seminar\n\nLect
 ure held in Room 2-143 in the Simons Building (building 2).\n\nAbstract\nG
 iven a compactly supported probability measure on the reals\, we will give
  a necessary and sufficient condition for there to be a sequence of totall
 y real algebraic integers whose distribution of conjugates approaches the 
 measure. We use this result to prove that there are infinitely many totall
 y positive algebraic integers X satisfying tr(X)/deg(X) < 1.899\; previous
 ly\, there were only known to be infinitely many such integers satisfying 
 tr(X)/deg(X) < 2. We also will explain how our method can be used in the s
 earch for simple abelian varieties with extreme point counts.\n
LOCATION:https://researchseminars.org/talk/MITNT/63/
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