Wed, April 20, 2022
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April 2022
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11:00am [11:30am] Aditya Karnataki
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.

4:00pm [4:00pm] Professor Parthanil Roy
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).