Lectures on algebraic stacks

Tuesday, 3 Oct.  11.30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (retd)

Title: Algebraic stacks

Topology and Related Topics Seminar

Tuesday, 3  October  2023, 2:30 pm

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Venue: Room 215

Host: Rekha Santhanam

Speaker: Bittu Singh

Affiliation: IIT Bombay

Title: Quillen stratification theorem

Abstract:  In our previous sessions, we have successfully constructed the universal bundle and demonstrated the equivalence between two definitions of group cohomology from both algebraic and topological perspectives. In this talk, I will present the proof of a theorem, which asserts that if the total space of a principal G-bundle is aspherical, it is indeed the universal bundle. Additionally, I will introduce another approach to constructing the universal G-bundle using simplicial sets, an approach attributed to Milnor.

Lecture series on Hodge Theory

Wednesday and Thursday, 11.30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Hodge Theory

Abstract:  These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will discuss the Kahler condition, and its consequences (Kahler identities etc.).

IITB Analysis Seminar

Wednesday, 4 Oct, 2 pm - 3 pm

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Venue: Ramanujan Hall

Host: Chandan Biswas

Abstract: This is the organizational meeting for the regular analysis (PDE, Harmonic analysis, Operator theory, Probability) seminar in the department. The goal of this meeting is to discuss a possible schedule (day of the week and time of the talks) and if possible, a list of upcoming speakers.

Lecture series on Hodge Theory

Wednesday and Thursday, 11.30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Hodge Theory

Abstract:  These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will discuss the Kahler condition, and its consequences (Kahler identities etc.).

Topology and Related Topics Seminar

Thursday  5th October  2023, 3:30 pm

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Venue: 216

Host: Rekha Santhanam

Speaker: Aparajita Karmakar

Affiliation: ISI Kolkata 

Title:  Results on equivariant cohomology of projective spaces.

Abstract: In this talk, I will discuss some basic notions in equivariant cohomology theory to finally present our work where we have calculated the equivariant additive homology decompositions of complex projective spaces. Following Lewis's approach for Burnside ring coefficients, we have been able to calculate the equivariant cohomology ring structure of projective spaces with integer coefficients. I will try to present these results and some of their applications.

Commutative Algebra seminar

Thursday, 5 Oct. 3.30-5.00 pm

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Venue: Ramanujan Hall

Host: Tony Puthenpurakal

Speaker: Jugal Verma, IIT Bombay

Title: Local cohomology  and Hilbert functions-1

Abstract: In this series of four lectures, I will prove the Grothendieck-Serre (GS)  formula for the difference between the Hilbert function and the Hilbert polynomial of a graded module over a standard graded ring. I will also prove some of its variations for the Hilbert-Samuel polynomial using the local cohomology of Rees algebras. The first lecture will review the basic results of local cohomology modules needed for the later lectures. An important invariant of the Hilbert function is its postulation number. We will see that the Castelnuovo-Mumford regularity is an upper bound on the postulation number. In the later lectures, we shall show how the GS -formula yields unified proofs of many results due to Sally, Rossi-Valla, and Huneke-Ooishi, about Hilbert-Samuel polynomial of m-primary ideals in local rings.

IITB Analysis Seminar

Thursday, 5th Oct, 5:15 pm - 6:15 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 first of a series of weekly talks to be held on Thursday afternoon. We will discuss the basic tools that are used in Fourier restriction estimates, and the primary goal is to try to understand the proof of the current best bound (due to Larry Guth 2014, and Hong Wang, Shukun Wu, 2022) for the “simplest case” of the Fourier restriction conjecture associated with the two-dimensional paraboloid in $\R^3$.