[iasmath-semru] Mathematics Seminars -- Week of September 11, 2017

[Anthony Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of September 11, 2017


--------------
To view mathematics in titles and abstracts, please click on the talk's link.
--------------

Thursday, September 14

Working Group on Algebraic Number Theory
Speaker: 	To Be Announced
Time/Room: 	2:00pm - 4:00pm/S-101

Joint IAS/Princeton University Number Theory Seminar
Topic: 		\(2^\infty\)-Selmer groups, \(2^\infty\)-class groups, and Goldfeld's conjecture
Speaker: 	Alex Smith, Harvard University
Time/Room: 	4:30pm - 5:30pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=132404

1 \(2^\infty\)-Selmer groups, \(2^\infty\)-class groups, and Goldfeld's 
conjecture
    Alex Smith

Take \(E/Q\) 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 \(2^{k+1}\)-class groups of the quadratic imaginary fields are 
distributed as predicted by the Cohen-Lenstra heuristics for all \(k > 1\).

http://www.math.ias.edu/seminars/abstract?event=132404

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars