NTS/Abstracts
Aug 28
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Sep 04
| Patrick Allen |
| Unramified deformation rings |
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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
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Sep 18
| Takehiko Yasuda |
| Distributions of rational points and number fields, and height zeta functions |
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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 |
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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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