


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. 3.305.00 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: Jugal Verma, IIT Bombay
Title: Local cohomology and Hilbert functions1
Abstract: In this series of four lectures, I will prove the GrothendieckSerre (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 HilbertSamuel 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 CastelnuovoMumford 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, RossiValla, and HunekeOoishi, about HilbertSamuel polynomial of mprimary 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 twodimensional paraboloid in $\R^3$.