Sep 08  Marco Sangiovanni Vincentelli (Princeton)

A Unified Framework for the Construction of Euler Systems
Euler Systems (ESs) are collections of Galois cohomology classes that verify some corestriction compatibilities. The key feature of ESs is that they provide a way to bound Selmer groups, thanks to the machinery developed by Rubin, inspired by earlier work of Thaine, Kolyvagin, and Kato. In this talk, I will present joint work with C. Skinner, in which we develop a new method for constructing Euler Systems and apply it to build an ES for the Galois representation attached to the symmetric square of an elliptic modular form. I will stress how this method gives a unifying approach to constructing ESs, in that it can be successfully applied to retrieve most classical ESs (the cyclotomic units ES, the elliptic units ES, Kato's ES, LeiLoefflerZerbes ES for the RankinSelberg convolution of two elliptic modular forms...).

Sep 15  Tongmu He (IAS)

Sen Operators and Lie Algebras arising from Galois Representations over $p$adic Varieties
Any finitedimensional padic representation of the absolute Galois group of a padic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their construction to the fundamental group of a padic affine variety with a semistable chart, and prove that the module of Sen operators is canonically defined, independently of the choice of the chart. When the representation comes from a Q_prepresentation of the fundamental group, we relate the infinitesimal action of inertia subgroups with Sen operators, which is a generalization of a result of Sen and Ohkubo. These Sen operators can be extended continuously to certain infinitedimensional representations. As an application, we prove that the geometric Sen operators annihilate locally analytic vectors, generalizing a result of Pan.

Sep 22  Preston Wake (Michigan State)

Rational torsion in modular Jacobians
For a prime number N, Ogg's conjecture states that the torsion in the Jacobian of the modular curve X_0(N) is generated by the cusps. Mazur proved Ogg's conjecture as one of the main theorems in his "Eisenstein ideal" paper. I'll talk about a generalization of Ogg's conjecture for squarefree N and a proof using the Eisenstein ideal. This is joint work with Ken Ribet.

Sep 29  Joe KramerMiller (Lehigh)

Geometric Iwasawa theory and $p$adic families of motives over function fields
Geometric Iwasawa theory studies the behavior of padic towers of curves. Classically, the focus has been on the ppart of class groups, mirroring Iwasawa theory for number fields. However, there are many interesting features of Iwasawa theory for curves that have no number field analogy. The ppart of the class group is only a small part of the pdivisible group, a much more intricate object with no number field analogy. In this talk I will survey various results and conjectures about the behavior of pdivisible groups along towers of curves. I will also discuss what geometric Iwasawa theory for motives should look like and explain new results in this direction.

Oct 06  Daxin Xu (MCM)

$p$adic nonabelian Hodge theory over curves via moduli stacks
The $p$adic Simpson correspondence aims to establish an equivalence between generalized representations and Higgs bundles over a $p$adic variety. In this talk, we will explain how to upgrade such an equivalence to a twisted isomorphism of moduli stacks in the curve case. This is based on a joint work in progress with Heuer.

Oct 13  Sean Howe (Utah)


Oct 20  Ziquan Yang (Wisconsin)


Oct 27  Michel Gros (Université de Rennes 1)


Nov 03  TsaoHsien Chen (Minnesota)


Nov 10  Xinwen Zhu (Stanford)


Nov 17  Rebecca Bellovin (Glasgow)


Dec 01  Deepam Patel (Purdue)


Dec 08  Peter Xu (UCLA)

