


Topology and Related Topics Seminar
Tuesday, 12 September 2023, 2.30 3:45 pm
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Venue: Ramanujan Hall
Host: Rekha Santhanam
Speaker: Bittu Singh
Affiliation: IIT Bombay
Title: Quillen stratification theorem"
Abstract: In the 1st talk I'll describe group cohomology,
restrictions transfer, LHS and Quillen Venkov Lemma.
Seminar on Analysis of PDE
Tuesday, 12 September 2023, 04.00 pm
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Venue: Room 113, Department of Mathematics
Host: Harsha Hutridurga
Speaker: Bikram Bir
Affiliation: IIT Bombay
Title: A Splitting Discontinuous Galerkin Finite Element Method for the VlasovNavierStokes equation.
Abstract: In this talk, we shall discuss a splitting algorithm that we have developed to simulate
solutions to a twophase flow model arising in the study of aerosols.
Algebraic Groups seminar
Tuesday, 12 September 2023, 4 pm
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Venue: Ramanujan Hall
Host: Shripad Garge
Speaker: Chayan Karmakar
Affiliation: IIT Bombay
Title: Differentials & smooth points  II
Abstract: We study differentials with the aim of introducing Lie algebras for algebraic groups.
Commutative Algebra Seminar
Tuesday. 5 September, 4 pm

Venue: Room 215
Host: Tony Puthenpurakal
Speaker: Tony Puthenpurakal
Affiliation: IIT Bombay
Title: Triangulated and Derived CategoriesVI
Abstract: We conclude our introduction to Triangulated categories.
Representation Theory seminar
Wednesday, 13 September 2023, 9:30 am
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Venue: Mini Conference Room
Host: U. K. Anandavardhanan
Speaker: Mohammed Saad Qadri
Affiliation: IIT Bombay
Title: On Higher Multiplicity upon Restriction from GL(n) to GL(n−1)
Abstract:
Let $F$ be a nonarchimedean local field. Let $\Pi$ be a principal series representation of $\GL_n(F)$ induced from a cuspidal representation of a Levi subgroup. When $\pi$ is an essentially square integrable representation of $\GL_{n1}(F)$ we prove that $\Hom_{\GL_{n1}}(\Pi,\pi)$ $= \mathbb{C}$ and $\Ext^i_{\GL_{n1}}(\Pi,\pi) = 0$ for all integers $i\geq 1$, with exactly one exception (up to twists), namely, when $\Pi= \nu^{(\frac{n1}{2})} \times \nu^{(\frac{n3}{2})} \times \ldots \times \nu^{(\frac{n1}{2})}$ and $\pi$ is the Steinberg. When $\Pi= \nu^{(\frac{n1}{2})} \times \nu^{(\frac{n3}{2})} \times \ldots \times \nu^{(\frac{n1}{2})}$ and $\pi$ is the Steinberg of $\GL_{n1}(F)$, then $\dim \Hom_{\GL_{n1}(F)}(\Pi,\pi)=n$. We also exhibit specific principal series for which each of the intermediate multiplicities $2, 3, \cdots, (n1)$ are attained.
Along the way, we also give a complete list of those irreducible nongeneric representations of $\GL_{n}(F)$ that have the Steinberg of $\GL_{n1}(F)$ as a quotient upon restriction to $\GL_{n1}(F)$. We also show that there do not exist nongeneric irreducible representations of $\GL_{n}(F)$ that have the generalized Steinberg as a quotient upon restriction to $\GL_{n1}(F)$.
Lecture series on Hodge Theory
Wednesday and Thursday
13 and 14 September, 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.
We will finish the proof of the de Rham theorem, via sheaf cohomology, and discuss some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.
CACAAG seminar
Wednesday, 13 September, 5:30 PM
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Venue: Ramanujan Hall.
Host: Madhusudan Manjunath
Speaker: Madhusudan Manjunath, IIT Bombay
Title: The Chow Ring of a Simplicial Toric Variety IV.
Abstract: We will continue our study of the Chow ring of a simplicial toric variety.
Lecture series on Hodge Theory
Wednesday and Thursday
13 and 14 September, 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.
We will finish the proof of the de Rham theorem, via sheaf cohomology, and discuss some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.
Lecture series on algebraic stacks
Friday, 15 September, 11:30 am

Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker : Nitin Nitsure
Affiliation: TIFR, Mumbai (retd)
Title: Fibered groupoids and stacks.
Abstract: Schemes can be understood via their functors of points. Descent theory shows that these functors are big etale sheaves over Spec Z. Amongst such sheaves, schemes and algebraic spaces are characterized by further 'algebraicity' conditions. Similarly, algebraic stacks are fibered groupoids which are stacks, which are the analogue of the sheaf and descent conditions. A further 'algebraicity' condition defines algebraic stacks. In the next few lectures, we will look at fibered groupoids and stacks, and give many examples. This will prepare the ground for introducing the algebraicity conditions that characterize algebraic stacks.