Tue, September 26, 2023
Public Access

Category: All

September 2023
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10:00am [10:30am] Omkar Javadekar, IIT Bombay
Annual Progress Seminar

Tuesday, 26 September 2023, 10.30 - 11.30 am


Venue: Room 113

Host: Ananthnarayan H.

Speaker: Omkar Javadekar

Affiliation: IIT Bombay

Title: Associated Graded Modules and Pure Resolutions

Abstract: Given a finitely generated module M over a Noetherian local 
ring R, one would like to know when the corresponding associated graded 
module G(M) has a pure resolution over the associated graded ring G(R). 
In this talk, we will construct a complex F* of free G(R)-modules using 
a minimal free resolution F of M over R, and show that F* is a minimal 
free resolution of G(M) if and only if G(M) is pure. We will apply this 
result to give sufficient conditions for R to be Cohen-Macaulay, and 
also prove a local version of Herzog-Kuhl equations.

2:00pm [2:30pm] Bittu Singh, IIT Bombay
Topology and Related Topics Seminar

Tuesday, 26  Sept 2023, 2:30 pm


Venue: Ramanujan Hall

Host: Rekha Santhanam

Speaker: Bittu Singh

Affiliation: IIT Bombay

Title: Quillen stratification theorem

Abstract: This is the second talk. Here I will describe the topological 
aspect of group cohomology, the Equivalence of the algebraic and 
topological definitions.

Then I will move to L-H-S and Quillen Venkov Lemma.

3:00pm [3:00pm] Sayed Sadiqul Islam, IIT Bombay

Annual Progress Seminar

TuesdaySeptember 26, 3 pm-4 pm


Venue: Room-215

Host: Tony J. Puthenpurakal

Speaker: Sayed Sadiqul Islam

Title: Reductions of ideals in local rings

Abstract: The reduction theory goes back to the influential 1954 paper by Northcott and Rees, the paper that introduced the basic notions. We will prove the existence of minimal reductions and will discuss some properties of minimal reductions. A closely related notion is that of analytic spread l(I) of I is defined to be the Krull dimension of the fiber cone of I. We will see how analytic spread behaves in some special cases. If time permits then will introduce some new notions. 


4:00pm [4:00pm] Chayan Karmakar, IIT Bombay
Algebraic Groups seminar

Tuesday, 26 September 2023, 4 pm


Venue: Ramanujan Hall

Host: Shripad Garge

Speaker: Chayan Karmakar

Affiliation: IIT Bombay

Title: Differentials & Smooth Points - III
Abstract: We study smooth points on a variety and will try to introduce 
the notion of Lie algebra of a linear algebraic group.