


Lecture series on algebraic stacks
Monday, 28 August, 11:30 am1.00 pm

Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker : Nitin Nitsure
Affiliation: TIFR, Mumbai (retd)
Title: Algebraic spacesII
Abstract: In his talk `The Implicit Function Theorem in Algebraic Geometry', delivered at the legendary conference `Algebraic Geometry, Bombay1968', Michael Artin expanded the category of spaces used in algebraic geometry by introducing `algebraic spaces', which was a step beyond the schemes of Grothendieck. In the 55 years that have passed since then, algebraic spaces have become an important part of Algebraic Geometry. In particular, the theory of algebraic stacks makes foundational use of them.
In this lecture, we will introduce algebraic spaces, just assuming that the audience is familiar with schemes at the level of the first few sections of Chapter 2 of Hartshorne's textbook Algebraic Geometry'. After giving some motivation and examples, some basic properties of algebraic spaces will be outlined.
This lecture is the beginning of a series of about 12 talks titled `An Introduction to Algebraic Stacks'. The aim of this series is to cover the first half of the textbook `Champs Algebriques' by Laumon and MoretBailly. This knowledge is essential in order to follow a whole lot of modern research in both arithmetic and geometry.
Commutative Algebra Seminar
Tuesday, August 29, 3:30 pm4.30 pm

Venue: Room 215
Host: Tony Puthenpurakal
Speaker: Tony Puthenpurakal, IIT Bombay
Title: Triangulated and Derived Categories 3
Abstract: We continue our introduction to Triangulated categories.
Algebraic Groups seminar
Tuesday, 29 August 2023, 4 pm
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Venue: Ramanujan Hall
Host: Shripad Garge
Speaker: Chayan Karmakar
Affiliation: IIT Bombay
Title: Derivations and Tangent Spaces  III
Abstract: We study derivations with the aim of introducing Lie algebras for algebraic groups.
Lecture series on Hodge Theory
Wednesday and Thursday
30 and 31 August, 11:30 am – 1.00 pm

Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker: V. Srinivas
Affiliation: IIT Bombay
Title: Introduction to Hodge Theory
Abstract: These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.
Mathematics Colloquium
Wednesday, 30 August at 4.005.00 pm
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Venue: Ramanujan Hall
Host: Saikat Mazumdar
Speaker: Adimurthi, IIT Kanpur and TIFRCAM, Bengaluru
Title: Critical Fractional Laplacian
Abstract: Dyda obtained the embedding of the space of functions having finite Fractional Laplacian norm in his work. He has not covered the critical case and asked several questions. In this talk, I will explain his questions and how they can be handled. This is a joint work with Prosenjit, Purbita, and Vivek Sahu.
CACAAG Seminar
Wednesday, 30 August, 5:30 PM

Venue: Ramanujan Hall.
Host: Madhusudan Manjunath
Speaker: Madhusudan Manjunath, IIT Bombay.
Title: The Chow Ring of a Simplicial Toric Variety II.
Abstract: We will continue our study of the Chow ring of a simplicial toric variety.
Lecture series on Hodge Theory
Wednesday and Thursday
30 and 31 August, 11:30 am – 1.00 pm

Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker: V. Srinivas
Affiliation: IIT Bombay
Title: Introduction to Hodge Theory
Abstract: These are part of an ongoing series of lectures on the basics of Hodge theory. The next two lectures will finish the proof of the de Rham theorem, via sheaf cohomology, and if time permits, a beginning will be made on some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.
Topology and Related Topics
Thursday, 31 August 2023, 2.30 pm
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Venue: Room 215
Host: Rekha Santhanam
Speaker: Soumyadeb Samanta
Affiliation: IIT Bombay
Title: An Introduction to Riemannian Manifolds (contd.)
Abstract: This talk will be in continuation with the previous one. I plan to cover the following: geodesics, curvature, Jacobi fields, and variation formulas.