April 2022
Public Access Category: All |

- Time:
- 5:30pm
- Description:
- Speaker: Alessandro De Stefani, Università di Genova, Italy.

Date/Time: 15 April 2022, 5:30pm IST/ 12:00pm GMT / 8:00am ET (joining

time 5:15pm IST).

Gmeet link: meet.google.com/qxw-gahn-kiw

Title: A uniform Chevalley theorem for direct summands in mixed

characteristic.

Abstract: Let R be a graded direct summand of a positively graded

polynomial ring over the p-adic integers. We exhibit an explicit constant

D such that, for any positive integer n and any homogeneous prime ideal Q

of R, the Dn-th symbolic power of Q is contained in the n-th power of the

homogeneous maximal ideal (p)R + R_+. The strategy relies on the

introduction of a new type of differential powers, which do not require

the existence of a p-derivation on R. The talk will be based on joint work

with E. Grifo and J. Jeffries.

For more information and links to previous seminars, visit the website of

VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 11:30am
- Description:
- 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:
- 4:00pm
- Description:
- Geometric Analysis seminar series.

https://sites.google.com/math.iitb.ac.in/geometric-analysis/home

Speaker: Ali Hyder (TIFR-CAM Bangalore)

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

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No 215, Department of Mathematics
- Description:
- Representation theory and Algebraic Geometry seminar' reading group.

Speaker: Suraj Panigrahy

Here are the details:

DDT: Tuesday, 26th April, 2:30 – 3:45 pm

Venue : Lecture hall 215, Department of mathematics.

Title: Bezout's Theorem

Abstract: Named after Étienne Bézout, The Bezout's Theorem states that in

the Complex Projective Plane two polynomials curves(without any common

factors) intetsect at atmost mn points(counting multiplicity), where m, n

are the degrees of the two polynomials.

To prove this result, we will see basics of Algebraic Geometry and/or

Projective Geometry.

We have now a dedicated website where one can find the notes and resources

from the past meets and announcements of the upcoming meetings:

https://sites.google.com/view/rtag/

Next two weeks there is an ATM school on Intersection theory happening at

IIT.

https://www.atmschools.org/school/2022/NCMW/it/speakers-and-syllabus

For the same, we will not have talks in our seminar during this period.

Please join us today !

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: A Gentle Survey of Class Groups.

Speaker: Dipendra Prasad.

Time: 5pm, Wednesday, 27 April, 2022.

Venue: Ramanujan Hall, Mathematics Department.

Abstract: We survey various aspects of class groups of number fields,

concluding with Cohen-Lenstra heuristics. These are heuristics regarding

the distribution of class groups.