NTS/Abstracts

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Aug 28

Robert Lemke Oliver
https://www.math.wisc.edu/wiki/index.php/NTS/Abstracts#Sep_04

Bhargava and Shankar have shown that the average size of the 2-Selmer 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 two-torsion 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 pro-p abelian extensions of a number field are infinitely ramified above p. Boston conjectured a nonabelian analogue of this fact, predicting that certain universal p-adic representations that are unramified at p act via a finite quotient, and this conjecture strengthens the unramified version of the Fontaine-Mazur conjecture. We show in many cases that one can deduce Boston's conjecture from the unramified Fontaine-Mazur conjecture, which allows us to deduce (unconditionally) Boston's conjecture in many two-dimensional cases. This is joint work with F. Calegari.



Sep 11

Melanie Matchett Wood
TBD

TBD



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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