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DTSTAMP:20180312T085003Z
DTSTART;TZID=America/Los_Angeles:20180312T151000
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SUMMARY:Arithmetic Geometry and Number Theory RTG Seminar: $2^k$-Selmer groups\, $2^k$-class groups\, and Goldfeld's conjecture
UID:116261-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:748 Evans Hall
DESCRIPTION:Alexander Smith\, Harvard University\n\nTake $E/\\mathbb Q$ to be an elliptic curve with full rational 2-torsion (satisfying some extra technical assumptions). In this talk\, we will show that $100\\%$ of the quadratic twists of $E$ have rank less than two\, thus proving that the BSD conjecture implies Goldfeld's conjecture in these families. To do this\, we will extend Kane's distributional results on the 2-Selmer groups in these families to $2^k$-Selmer groups for any $k >1$. In addition\, using the close analogy between $2^k$-Selmer groups and $2^{k+1}$-class groups\, we will prove that the $2^k$-class groups of the quadratic imaginary fields are distributed as predicted by the Cohen-Lenstra heuristics for all $k > 1$.\n\nSeminar Format: The seminar consists of two 50-minute talks\, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00)\, with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory\; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=116261&view=preview
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