Difference between revisions of "NTS ABSTRACT"
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 bgcolor="#BCD2EE" align="center"  Bounds on the 2torsion in the class groups of number fields   bgcolor="#BCD2EE" align="center"  Bounds on the 2torsion in the class groups of number fields  
    
−   bgcolor="#BCD2EE"   +   bgcolor="#BCD2EE"  (Joint with M. Bhargava, T. Taniguchi, F. Thorne, J. Tsimerman, Y. Zhao) 
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+  Given a number field K of fixed degree n over Q, a classical theorem of BrauerSiegel asserts that the size of the class group of K is bounded by O_\epsilon(Disc(K)^(1/2+\epsilon). For any prime p, it is conjectured that the ptorsion  
+  subgroup of the class group of K is bounded by O_\epsilon(Disc(K)^\epsilon. Only the case n=p=2 of this conjecture in known. In fact, for most pairs (n,p), the best known bounds come from the "convex" BrauerSiegel bound.  
+  
+  In this talk, we will discuss a proof of a subconvex bound on the size of the 2torsion in the class groups of number fields, for all degrees n. We will also discuss an application of this result towards improved bounds on the number of integral points on elliptic curves.  
}  }  
</center>  </center> 
Revision as of 16:05, 18 January 2017
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Contents
Jan 19
Bianca Viray 
On the dependence of the BrauerManin obstruction on the degree of a variety 
Let X be a smooth projective variety of degree d over a number field k. In 1970 Manin observed that elements of the Brauer group of X can obstruct the existence of a kpoint, even when X is everywhere locally soluble. In joint work with Brendan Creutz, we prove that if X is geometrically abelian, Kummer, or bielliptic then this BrauerManin obstruction to the existence of a kpoint can be detected from only the dprimary torsion Brauer classes. 
Jan 26
Speaker 
title 
abstract

Feb 2
Arul Shankar 
Bounds on the 2torsion in the class groups of number fields 
(Joint with M. Bhargava, T. Taniguchi, F. Thorne, J. Tsimerman, Y. Zhao)
Given a number field K of fixed degree n over Q, a classical theorem of BrauerSiegel asserts that the size of the class group of K is bounded by O_\epsilon(Disc(K)^(1/2+\epsilon). For any prime p, it is conjectured that the ptorsion subgroup of the class group of K is bounded by O_\epsilon(Disc(K)^\epsilon. Only the case n=p=2 of this conjecture in known. In fact, for most pairs (n,p), the best known bounds come from the "convex" BrauerSiegel bound. In this talk, we will discuss a proof of a subconvex bound on the size of the 2torsion in the class groups of number fields, for all degrees n. We will also discuss an application of this result towards improved bounds on the number of integral points on elliptic curves. 
Feb 9
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Feb 16
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Feb 23
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Mar 2
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Mar 9
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Mar 16
Mar 30
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Apr 6
Celine Maistret 
Apr 13
Apr 20
Yueke Hu 
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Apr 27
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May 4
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