Title: Commutators and commutator subgroups in finite p-groups.
Speaker : Rahul Kaushik
Time : 11:30-12:30
Date : 18th April (Monday)
Link : https://meet.google.com/bmi-aoav-tgi?authuser=0
Titile:
Commutators and commutator subgroups in finite p-groups
Let G be a finite group and K(G) := {[a, b] | a, b ∈ G}. It is well known that
the commutator subgroup γ2(G) of G is generated by K(G). A natural question that has attracted the attention of many mathematicians over last many decades is whether γ2(G) is equal to K(G) or not for groups G in a given class of groups.
Ore Conjectured that K(G) = γ2(G) for all finite simple groups G(proved in 2010).
This problem has been studied for different classes of groups. Our interest here is in
the groups of prime power order. It is planned, in this talk, to survey some relevant
literature and present our work along the above mentioned theme. We will give
a classification of finite p-groups G having γ2(G) of order p4 and exponent p such
that K(G) 6= γ2(G). Along with this we also present a complete characterisation of groups G of order p7 for which K(G) 6= γ2(G), and indicate further research directions suggested by our work.
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).
Time: April 21, Thursday, 4:00 pm (Indian Standard Time)
Title: Blow-up analysis and partial regularity results for Liouville type
equations
Abstract: Due to the presence of the exponential nonlinearity, the Liouville equation in dimension three and higher is supercritical. In particular, it admits several singular solutions. We will talk about
asymptotic behavior of a family of stationary solutions, and how to use it to obtain partial regularity results.
Google Meet joining info
Video call link: https://meet.google.com/pho-dpdy-vtz
Or dial: (US) +1 775-442-4580 PIN: 999 128 364#
Time:
5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Title: Avatars of Picard.
Time: 22 April, 5pm.
Venue: Ramanujan Hall.
Speaker: Madhusudan Manjunath.
Abstract: This talk will be an overview of the seminar. The seminar will cover Picard groups in its various manifestations, as associated to number fields, algebraic varieties, graphs and tropical curves. Future speakers include Prof. Saurav Bhaumik and Prof. Dipendra Prasad.
Time:
5:30pm
Description:
Speaker: Yuji Yoshino, Okayama University, Japan.
Date/Time: 22 April 2022, 5:30pm IST/ 12:00pm GMT / 8:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/fpc-wvwk-asp
Title: Naive liftings of dg modules.
Abstract: The naive lifting for dg modules is the new concept introduced by M.Ono, S.Nasseh and myself for the purpose of unifying the ideas of lifting and weak lifting for modules over commutative rings. In this talk I will show how we get the obstruction class of naive liftings, which in fact coincides with the Atiyah class that has been introduced by Buchweitz-Flenner. This is a joint work with Saeed Nasseh and Maiko Ono.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar