


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 Gbundles, where G is an algebraic group. The algebraic cohomology of this stack gives the algebraic cohomological version of the characteristic classes of principal Gbundles.
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, 4.005.00 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, 11.301.00
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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, 11.301.00
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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.