Lecture series on algebraic stacks
Monday 20 November, 11.30 am

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Venue: Room No 215, Department of Mathematics
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: 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.

Analysis and PDE seminar

Monday 20th Nov. 4 pm - 5 pm

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Venue: Ramanujan Hall

Host: Sanjay Pusti

Speaker: Ankit Bhojak
Affiliation: IISER Bhopal

Title: Sharp endpoint L^p-estimates for bilinear spherical maximal functions
Abstract: Attached.

Probability and Statistics Seminar

Thursday, 23  November  2023, 10:00 am

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Venue: Ramanujan hall

Host: Ayan Bhattacharya

Speaker: Souvik Dhara

Affiliation: Purdue University 

Title: Community Detection with Censoring

Abstract: Recovering latent communities is a key unsupervised learning task in network data with applications spanning across a multitude of disciplines. For example, identifying communities in web pages can lead to faster searches, classifying regions of the human brain in communities can be used to predict the onset of psychosis, and identifying communities of assets can help investors manage risk by investing in different communities of assets. However, the scale of these massive networks has become so large that it is often impossible to work with the entire network data. In this talk, I will talk about some theoretical progress for community detection in a probabilistic setup especially when we have missing data about the network. Based on joint works with Julia Gaudio, Elchanan Mossel, and Colin Sandon.

Analysis and PDE seminar

Thursday 23rd Nov. 3 pm - 4 pm

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Venue: Ramanujan Hall

Host: Chandan Biswas

Speaker: Chandan Biswas
Affiliation: IIT Bombay

Title:  A basic introduction to Fourier restriction estimate.
Abstract: We will finish our discussion on restriction onto the moment curve.

Lecture series on algebraic stacks
Monday 24 November, 11.30 am
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Venue: Ramanujan Hall
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (Retd)

Title: An Introduction to Gerbes

Abstract: Gerbes (for good reason) have become very fashionable objects in algebra, algebraic geometry, differential topology, and physics. Algebraists come across them for example in their study of Brauer groups (see Milne `Etale Cohomology' Chapter 4). Differential geometers study connections on these and their relation to characteristic classes. These feature in the works, for example, of Hitchin, Brylinski, Breen, etc. I will not be able to say anything about the physics applications. Gerbes are very important (in many ways) in Algebraic Geometry. This lecture will give an introduction to the subject. The basic technology of gerbes involves Stacks, and that is why this talk is in the ongoing series on Algebraic Stacks.

Combinartorics and TCS seminar

Friday, 24 November 11.30 am

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Venue: Ramanujan Hall

Host: Niranjan Balachandran

Speaker: Shagnik Das

Affiliation: National University of Taiwan

Title: Covering grids with multiplicity

Abstract: It is a fairly simple exercise to determine the minimum number of
hyperplanes needed to cover all the points of a finite grid $S_1 \times S_2 \times \dots \times S_d \in \mathbb{F}^d$. However, the situation becomes much more complex if you add the condition that one of the points of the grid must be avoided, leading to a classic problem in combinatorial geometry. This was resolved by Alon and Füredi in a classic result that popularised the use of algebraic methods in combinatorics.  The recent work of Clifton and Huang, in which they considered the question a variant of the problem where the nonzero points of a hypercube should be covered multiple times while avoiding the origin, brought renewed interest to this problem. In addition to Alon-Füredi-style algebraic arguments, they used linear programming to asymptotically resolve the problem in certain ranges. Despite all the attention this problem has received, there remain many open problems, even in the case of two-dimensional grids over $\mathbb{R}$. In this talk, after surveying the background and introducing the techniques used, we shall present some recent results that resolve the problem for almost all two-dimensional grids.  The new results are joint work with Anurag Bishnoi, Simona Boyadzhiyska, and Yvonne den Bakker, and separately with Valjakas Djaljapayan, Yen-Chi Roger Lin, and Wei-Hsuan Yu.