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SUMMARY:Jeffrey Hatley (Union College)
DTSTART:20260428T200000Z
DTEND:20260428T210000Z
DTSTAMP:20260422T173343Z
UID:FCNTS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/29/">R
 anks of elliptic curves in quadratic twist families via Iwasawa theory</a>
 \nby Jeffrey Hatley (Union College) as part of Five College Number Theory 
 Seminar\n\nLecture held in Seeley Mudd 205 @Amherst College.\n\nAbstract\n
 For a fixed elliptic curve $E/\\mathbb{Q}$\, Goldfeld's Conjecture predict
 s that half of its quadratic twists have rank 0 and half have rank 1. This
  conjecture is now a theorem in most cases\, due to recent work of Alex Sm
 ith. However\, it is still interesting to ask for effective versions of th
 is theorem\; for instance\, if one considers only twists by prime numbers 
 which are 1 mod 4\, what can be said about the rank distribution? In this 
 talk\, we will discuss joint work with Anwesh Ray which uses Iwasawa theor
 y to study some of these sorts of questions.\n
LOCATION:https://researchseminars.org/talk/FCNTS/29/
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