Lecture series on algebraic stacks
Monday 30 October, 11.30 am

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Venue: Ramanujan Hall
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (Retd)

Title: The classifying stack BG for an algebraic group
Abstract: To any Lie group, there is classically associated a  topological space BG with the requisite universal property in the homotopy category of paracompact topological spaces. For example, for G = GL(n) the space BG is the infinite Grassmannian. However, when we go to the algebraic category (say schemes or algebraic spaces and their morphisms), such a space BG does not exist. This is a paradigmatic example where algebraic stacks rescue the situation. In this lecture, we will explain the construction of an algebraic stack BG which has the requisite universal property of classifying principal G-bundles, where G is an algebraic group. The algebraic cohomology of this stack gives the algebraic cohomological version of the characteristic classes of principal G-bundles.

Algebraic Groups Seminar

Tuesday, 31 October 2023, 4 pm
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Venue: Ramanujan Hall

Host: Shripad Garge

Speaker: Chayan Karmakar

Affiliation: IIT Bombay

Title: Lie algebras - II

Abstract: We introduce the notion of Lie algebra of a linear algebraic group. 

Commutative algebra seminar

Tuesday, 31 October, 4.00-5.00 pm

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Venue: Room 215

Host: J. K. Verma

Speaker: Kriti Goel

Affiliation: Basque Center for Applied Mathematics, Bilbao (Spain)

Title: Local cohomology of modular invariant rings

Abstract: Consider a finite group G acting on a polynomial ring R over a field. One of the fundamental problems of invariant theory is to establish a connection between the properties of the invariant ring R^G and the properties of the group action. While the situation is better understood when the order |G| of the group is a unit, much less is known otherwise. In this talk, we will explore some questions on the local cohomology modules of the ring of invariants in the situation where |G| is not a unit.  This is a joint work with Jack Jeffries (UNL) and Anurag Singh (University of Utah).

Lecture series on Hodge Theory

Wednesday, 1 November, 11.30-1.00

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Kahler condition and its consequences
Abstract: I will continue the sketch of the proof of the Hodge Theorem. After that, I will give some introduction to variation of Hodge structures, in a couple of lectures.

Lecture series on Hodge Theory

Thursday, 2 November, 11.30-1.00

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Kahler condition and its consequences

Abstract: I will continue the sketch of the proof of the Hodge Theorem. After that, I will give some introduction to variations of Hodge structures, in a couple of lectures.

Topology and Related Topics Seminar

Thursday, 2  November  2023, 2:30 -3:30 pm

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Venue: Room 215

Host: Rekha Santhanam

Speaker:  Aparajita Karmakar

Affiliation: ISI Kolkatta 

Title:  Regularity in Ring Spectra 

Abstract: In this talk, our goal will be to translate the notion of regularity in rings to regularity of ring spectra. Although the structural definition and the definition in terms of Ext can be extended for ring spectra, another equivalent definition of regularity involving finitely generated modules is not readily adaptable for spectra. 

Analysis and PDE seminar

Thursday, 2 Nov. 5.15 pm

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Venue: Ramanujan Hall
Host: Chandan Biswas

Speaker: Chandan Biswas, IIT Bombay

Title: A basic introduction to Fourier restriction estimates
Abstract: This is the fourth talk of the series. We will talk about Fourier restriction to the moment curve.