Time and Room: Monday 1:30 pm -3:00 pm BRNG 1206
Schedule:
Aug 24th: Speaker: Tong Liu : Overview BGK paper
Aug 31th: Speaker: Michael Wills: Review of crystalline and semisimple mod p representations of G_Q_p
Title: Introduction to crystalline and mod-p representations
Abstract: Arbitrary representations over Z_ell of the absolute Galois group of Q_p can be difficult to characterize when ell = p, in part because their reduction modulo p does not preserve the action of wild inertia. For an interesting subcategory of these, the crystalline representations, the action of inertia may be described via a filtration on a Qp-vector space. A recent preprint of Bhatt--Gee--Kisin describes a connection between a crystalline representation's associated filtration and the representation's reduction modulo p. This talk is the second in a learning seminar aimed at understanding this preprint, and will introduce the basics of both crystalline and mod-p representations of Q_p.
Sept 14th: Speaker: Ruipeng Zou: Affine Weyl groups
Title: Up-arrow ordering and affine Grassmannians
Abstract: Let $G$ be a split connected reductive group. We will go over the up arrow order on coweights and alcoves in the affine Weyl group. We explain its relationship with the Bruhat order, including Wang's theorem identifying the upper-arrow order on dominant alcoves with Bruhat order, and the resulting description of the upper-arrow order on dominant coweights. We will also review the affine Grassmannian and study the $\mu_p$-fixed locus in the affine Grassmannian.
Sept 21st: Speaker: Ruipeng Zhou : Affine Grassmannin
Title: \mu_p-fixed locus and orbit closure of affine Grassmannians
Abstract: Let G be a split connected reductive group. In this talk, we will review the affine Grassmannian of G, its Cartan and Iwahori decompositions, and the associated Schubert stratifications. We will then study the \mu_p-fixed locus using affine flag varieties and parahoric subgroups. Finally, we will discuss the orbit-closure results using the upper-arrow order.
Sept 28th: Speaker: Varun Balasubramanian: Etale \varphi-modules
Oct. 5th: Speaker: Boqiang Zhang: Introduction of Kisin modules.
Oct. 19th: μ_p structure. Speaker: George Nicolas Diaz-Wahl
References:
Bhatt Gee and Kisin: Reduction modulo p of crystalline Galois representations via μ_p-equivariance.