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SUMMARY:Ross Paterson (University of Glasgow)
DTSTART:20210628T163000Z
DTEND:20210628T170000Z
DTSTAMP:20260423T052759Z
UID:POINT/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/37/">A
 verage Ranks of Elliptic Curves after $p$-Extension</a>\nby Ross Paterson 
 (University of Glasgow) as part of POINT: New Developments in Number Theor
 y\n\n\nAbstract\nAs $E$ varies among elliptic curves defined over the rati
 onal numbers\, a theorem of Bhargava and Shankar shows that the average ra
 nk of the Mordell--Weil group $E(\\mathbb{Q})$ is bounded.  If we fix a nu
 mber field $K$\, it is natural to then ask: is the average rank of $E(K)$ 
 also bounded in this family?  Moreover\, how does the average rank of $E(K
 )$ depend on $K$?\nThis talk will discuss recent progress on these questio
 ns for a restricted set of $K$.\n
LOCATION:https://researchseminars.org/talk/POINT/37/
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