Wed, April 20, 2022
Public Access Category: All |
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- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Aditya Karnataki
Date and time: Wednesday, April 20th at 11.30
Title : Families of (φ, τ)-modules and Galois representations
Abstract : Let K be a finite extension of ℚp. The theory of (φ, Γ)-modules constructed by Fontaine provides a good category to study p-adic representations of the absolute Galois group Gal(K/K). This theory arises from a ``devissage'' of the extension K/K through an intermediate extension K∞/K which is the cyclotomic extension of K. The notion of (φ, τ)-modules generalizes Fontaine's constructions by using Kummer extensions other than the cyclotomic one. It encapsulates the important notion of Breuil-Kisin modules among others. It is thus desirable to establish properties of (φ, τ)-modules parallel to the cyclotomic case. In this talk, we explain the construction of a functor that associates to a family of p-adic Galois representations a family of (φ, τ)-modules. The analogous functor in the (φ, Γ)-modules case was constructed by Berger and Colmez . This is joint work with Léo Poyeton.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Professor Parthanil Roy
Date: April 20, 2022
Time: 16.00 - 17.00
Venue: Ramanujan Hall at the Department of Mathematics.
Title: Amenable groups, von-Neumann algebras and ergodicity of stable
random fields
Abstract: In this work, it is established that the group measure space
construction corresponding to a minimal representation is an invariant
of a stationary symmetric stable random field indexed by any countable
group G. When G is amenable, we characterize ergodicity of stable fields
in terms of the central decomposition of this crossed product von
Neumann algebra coming from any (not necessarily minimal) Rosinski
representation. This shows that ergodicity is a W^*-rigid property (in a
suitable sense) for this class of fields.
The first part of this talk will focus on the following work of the
speaker: arXiv:2007.14821. The second part will be based on an ongoing
joint work with Mahan Mj (TIFR Mumbai) and Sourav Sarkar (University of
Cambridge).