


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 CohenMacaulay, and also prove a local version of HerzogKuhl equations.
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 LHS and Quillen Venkov Lemma.
Annual Progress Seminar
Tuesday, September 26, 3 pm4 pm
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Venue: Room215
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.
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.