October 23, 2023 - October 27, 2023
Public Access Category: All |
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- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lecture series on algebraic stacks
Monday 23 October, 11.30 am
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Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker: Nitin NitsureAffiliation: 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 G-bundles, where G is an algebraic group. The algebraic cohomology of this stack gives the algebraic cohomological version of the characteristic classes of principal G-bundles.
- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Number Theory Seminar
Monday, 23 October 2023, 14:30
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Venue: Ramanujan hall
Host: U. K. Anandavardhanan
Speaker: Anand Chitrao
Affiliation: TIFR Mumbai
Title: Reductions mod $p$ of semi-stable representations.
Abstract: We compute the reductions mod $p$ of irreducible two-dimensional semi-stable representations of the absolute Galois group $\GQp$ of $\Qp$. We use the compatibility with respect to reduction mod $p$ between the $p$-adic Local Langlands Correspondence and an Iwahori theoretic version of the mod $p$ Local Langlands Correspondence. By estimating certain logarithmic functions on $\Qp$ by polynomials on open subsets of $\Zp$, we compute the reductions mod $p$ completely for weights at most $p + 1$. We also state how this method can be used, in theory, to compute the reductions mod $p$ of semi-stable representations of arbitrarily large weights. In passing, we extend some results on Iwahori induction to the case of non-commutative Hecke algebras.
- Time:
- 11:30am-1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Lecture series on Hodge Theory
Wednesday, 25 October, 11.30-1.00
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Venue: Ramanujan Hall
Host: Sudarshan Gurjar
Speaker: V. Srinivas, IIT Bombay
Title: Kahler condition and its consequences
Abstract: In the next couple of talks, I will give a sketch of the proof of the Hodge theorem, that any smooth form can be expressed as a sum of a harmonic form and a form in the image of the Hodge Laplacian.
- Time:
- 2:30pm-3:45pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Topology and Related Topics Seminar
Thursday, 26 Oct. 2:30 pm - 3:45 pm
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Venue: Room 215
Host: Rekha Santhanam
Speaker: Omkar Javadekar
Affiliation: IIT Bombay
Title: A review of derived category and related topics-2
Abstract: We will continue the discussion on derived categories and the Hopkins-Neeman theorem for small R-complexes.
- Time:
- 3:15pm
- Location:
- Venue: https://meet.google.com/zrc-owyg-ukt
- Description:
Online Number Theory Seminar
Thursday, 26 October, 3.15 pm
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Venue: https://meet.google.com/zrc-owyg-ukt
Host: Ravi Raghunathan
Speaker: Aditi Savalia
Affiliation: IIT Gandhinagar
Title: Limitations to equidistribution in arithmetic progressions
Abstract: It is well known that prime numbers are equidistributed in arithmetic progressions. Such a phenomenon is also observed more generally for a class of arithmetic functions. A key result in this context is the Bombieri-Vinogradov theorem which establishes that the primes are equidistributed in arithmetic progressions “on average” for moduli $q$ in the range $q ≤ x^{1/2−\epsilon}$ for any $\epsilon > 0$. Building on the idea of Maier, Friedlander and Granville showed that such equidistribution results fail if the range of the moduli $q$ is extended to $q ≤ x/(log x)^B$ for any $B > 1$. We discuss variants of this result and give some applications. This is joint work with Akshaa Vatwani.
- Time:
- 4:00pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Commutative Algebra seminar
Thursday, 26 Oct. 4.00-5.30 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: Jugal Verma, IIT Bombay
Title: The Grothendieck-Serre formula for Hilbert functions
Abstract: We will prove the Grothendieck-Serre formula for Hilbert functions of finite graded modules over graded Noetherian rings.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups Seminar
Friday, 27 October 2023, 4 pm
===================Venue: Ramanujan Hall
Host: Shripad Garge
Speaker: Chayan Karmakar
Affiliation: IIT Bombay
Title: Lie algebras-I
Abstract: We introduce the notion of Lie algebra of a linear algebraic group.