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SUMMARY:Jeffrey Hatley (Union College)
DTSTART:20260428T200000Z
DTEND:20260428T210000Z
DTSTAMP:20260824T073634Z
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 Pioneer Valley Number Theor
 y Seminar\n\nLecture held in Seeley Mudd 205 @Amherst College.\n\nAbstract
 \nFor a fixed elliptic curve $E/\\mathbb{Q}$\, Goldfeld's Conjecture predi
 cts that half of its quadratic twists have rank 0 and half have rank 1. Th
 is conjecture is now a theorem in most cases\, due to recent work of Alex 
 Smith. However\, it is still interesting to ask for effective versions of 
 this theorem\; for instance\, if one considers only twists by prime number
 s which are 1 mod 4\, what can be said about the rank distribution? In thi
 s talk\, we will discuss joint work with Anwesh Ray which uses Iwasawa the
 ory to study some of these sorts of questions.\n
LOCATION:https://researchseminars.org/talk/FCNTS/29/
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