NTS/Abstracts: Difference between revisions
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 bgcolor="#F0A0A0" align="center" style="fontsize:125%"  '''Melanie Matchett Wood'''   bgcolor="#F0A0A0" align="center" style="fontsize:125%"  '''Melanie Matchett Wood'''  
    
 bgcolor="#BCD2EE" align="center"  The distribution of sandpile groups of random graphs   bgcolor="#BCD2EE" align="center"  The distribution of sandpile groups of random graphs *  
    
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The sandpile group is an abelian group associated to a graph, given as the cokernel of the graph Laplacian. An Erdős–Rényi random graph then gives some distribution of random abelian groups. We will give an introduction to various models of random finite abelian groups arising in number theory and the connections to the distribution conjectured by Payne et. al. for sandpile groups. We will talk about the moments of random finite abelian groups, and how in practice these are often more accessible than the distributions themselves, but frustratingly are not a priori guaranteed to determine the  The sandpile group is an abelian group associated to a graph, given as the cokernel of the graph Laplacian. An Erdős–Rényi random graph then gives some distribution of random abelian groups. We will give an introduction to various models of random finite abelian groups arising in number theory and the connections to the distribution conjectured by Payne et. al. for sandpile groups. We will talk about the moments of random finite abelian groups, and how in practice these are often more accessible than the distributions themselves, but frustratingly are not a priori guaranteed to determine the distribution. In this case however, we have found the moments of the sandpile groups of random graphs, and proved they determine the measure, and have proven Payne's conjecture.  
distribution. In this case however, we have found the moments of the sandpile groups of random graphs, and proved they determine the measure, and have proven Payne's conjecture.  
* ''This is officially a Probability seminar, but will occur in the usual NTS room B105 at a slightly earlier time, 2:25 PM.''  
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Revision as of 17:48, 28 August 2014
Aug 28
Robert Lemke Oliver 
The distribution of 2Selmer groups of elliptic curves with twotorsion 
Bhargava and Shankar have shown that the average size of the 2Selmer group of an elliptic curve over Q, when curves are ordered by height, is exactly 3, and Bhargava and Ho have shown that, in the family of curves with a marked point, the average is exactly 6. In stark contrast to these results, we show that the average size in the family of elliptic curves with a twotorsion point is unbounded. This follows from an understanding of the Tamagawa ratio associated to such elliptic curves, which we prove is "normally distributed with infinite variance". This work is joint with Zev Klagsbrun. 
Sep 04
Patrick Allen 
Unramified deformation rings 
Class field theory allows one to precisely understand ramification in abelian extensions of number fields. A consequence is that infinite prop abelian extensions of a number field are infinitely ramified above p. Boston conjectured a nonabelian analogue of this fact, predicting that certain universal padic representations that are unramified at p act via a finite quotient, and this conjecture strengthens the unramified version of the FontaineMazur conjecture. We show in many cases that one can deduce Boston's conjecture from the unramified FontaineMazur conjecture, which allows us to deduce (unconditionally) Boston's conjecture in many twodimensional cases. This is joint work with F. Calegari. 
Sep 11
Melanie Matchett Wood 
The distribution of sandpile groups of random graphs * 
The sandpile group is an abelian group associated to a graph, given as the cokernel of the graph Laplacian. An Erdős–Rényi random graph then gives some distribution of random abelian groups. We will give an introduction to various models of random finite abelian groups arising in number theory and the connections to the distribution conjectured by Payne et. al. for sandpile groups. We will talk about the moments of random finite abelian groups, and how in practice these are often more accessible than the distributions themselves, but frustratingly are not a priori guaranteed to determine the distribution. In this case however, we have found the moments of the sandpile groups of random graphs, and proved they determine the measure, and have proven Payne's conjecture.

Sep 18
Takehiko Yasuda 
Distributions of rational points and number fields, and height zeta functions 
In this talk, I will talk about my attempt to relate Malle's conjecture on the distribution of number fields with Batyrev and Tschinkel's generalization of Manin's conjecture on the distribution of rational points on singular Fano varieties. The main tool for relating these is the height zeta function. 
Sep 25
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Oct 02
Pham Huu Tiep 
Nilpotent Hall and abelian Hall subgroups 
To which extent can one generalize the Sylow theorems? One possible direction is to assume the existence of a nilpotent subgroup whose order and index are coprime. We will discuss recent joint work with various collaborators that gives a criterion to detect the existence of such subgroups in any finite group. 
Oct 09
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Oct 16
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Oct 23
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Oct 30
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Nov 06
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Nov 13
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Nov 20
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Nov 27
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Dec 04
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Dec 11
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Organizer contact information
Sean Rostami (srostami@math.wisc.edu)
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