Algebraic Stacks lecture series
Tuesday, 13 February, 11:30 AM

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Venue:  Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: Bhaskaracharya Pratishthana

Title: Separated and proper morphisms for algebraic stacks.

Abstract: We will begin by revisiting the valuative criteria for universal closedness and separateness for morphisms between schemes. This will be followed by interesting elementary examples that illustrate why these criteria do not directly apply to algebraic spaces and algebraic stacks. We will end with the modified criteria that apply to algebraic spaces and algebraic stacks.

Topology and Related Topics Seminar

Tuesday, 13 February, 12:00-1:00

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Venue: Ramanujan Hall (Hybrid Lecture) (Speaker will be online).

Host: Rekha Santhanam

Speaker: Suraj Krishna

Affiliation: Technion - Israel Institute of Technology

Title: Mapping tori in geometric group theory.

Abstract: In this talk, I will provide a gentle introduction to 
geometric group theory using the concept of mapping tori. Using pictures 
and examples, I will introduce the relevant topics and give a glimpse of 
some of the spectacular progress made by stalwarts like Bill Thurston. 
Additionally, I will mention some recent progress in the field, along 
with my forays.

This talk is a background lecture especially aimed at graduate students 
for the talk  Suraj Krishna will give the following Tuesday.
 

Commutative Algebra Seminar

Tuesday, 13 Feb, 3 pm—4 pm

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Venue:   Room 215

Host: Tony J. Puthenpurakal

Speaker: Sudeshna Roy

Affiliation: TIFR Bombay

Title:  Epsilon multiplicity in two-dimensional standard  graded algebras

Abstract: The notion of epsilon multiplicity, a generalization of the Hilbert-Samuel multiplicity, was introduced by B. Ulrich and J. Validashti to detect the integral dependence of arbitrary ideals. This invariant is difficult to handle as there are examples where it can be irrational and the epsilon function is very far from being polynomial-like. Let $A$ be a standard graded normal domain of dimension two over a field with the unique homogeneous maximal ideal $m$. Let $I$ be a homogeneous ideal in $A$. Our objective is to show that the epsilon multiplicity of $I$ is a rational number.

Algebraic Groups Seminar
Tuesday, February 13, 4 PM--5 PM
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Venue: Ramanujan Hall, Department of Mathematics
Host: Dipendra Prasad

Speaker: Mohammed Saad Qadri
Affiliation: IIT Bombay

Title: Regular elements in semi-simple algebraic groups

Abstract: We will discuss the paper by Robert Steinberg, Regular elements of semi-simple algebraic groups Publications mathématiques de l'I.H.É.S., tome 25 (1965), p. 49-80.

Commutative Algebra seminar

Tuesday, 13 February 4 pm-5 pm

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Venue: Ramanujan Hall

Host: J. K. Verma

Speaker: S. K. Khanduja

Affiliation: IISER Mohali

Title: Some well-known Irreducibility Criteria for polynomials over rationals and their generalizations

Abstract: We will review the classical irreducibility criteria of Eisenstein, Schoenemann, and Dumas, and then discuss their extensions using Newton polygons and the theory of valuations. We shall also present recently proved generalizations of the well-known

results of Schur as well as of Filaseta and Trifonov regarding the irreducibility of the truncated exponential polynomial and the Bessel polynomial. This talk is partly based on joint work with Ankita Jindal, Bablesh Jhorar, and Sanjeev Kumar.

Mathematics Colloquium:

Wednesday, 14  February  2023, 4:00 pm

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Venue: Ramanujan hall

Host: Ravi Raghunathan

Speaker: Manish Patnaik

Affiliation: University of Alberta

Title: Eisenstein series and some variants on Loop Groups

Abstract: We will first review some aspects of the reduction theory for loop groups studied by Howard Garland in the 1970s. Following this, we explain how features of the Siegel domains in this setting essentially force certain cuspidal Eisenstein series on loop groups to be entire functions, in stark contrast to the finite-dimensional situation. 

Switching to the case of function fields, we then introduce, following ideas of Braverman and Kazhdan, new “regularized” cuspidal Eisenstein series for loop groups. These series are no longer entire and their Fourier coefficients encode (finite-dimensional) automorphic L-functions that have previously remained inaccessible by the standard Langlands-Shahidi method.

Probability and statistics seminar

Wednesday, 14th Feb, 4 pm--5pm

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Venue: Room 113, Maths Dept

Host: Siuli Mukhopadhyay

Speaker: Subhra Sankar Dhar

Affiliation:   IIT Kanpur

Title: Inspecting discrepancy between multivariate distributions using half-space depth

 Abstract: In this talk, we inspect whether a multivariate distribution is different from a specified distribution or not AND two multivariate distributions are equal or not. In the course of this study, a graphical toolkit using well-known half-spaced depth is proposed, which is a two-dimensional plot, regardless of the dimension of the data, and it is even useful in comparing high-dimensional distributions. The simple interpretability of the proposed graphical toolkit motivates us to formulate test statistics to carry out the corresponding testing of hypothesis problems. It is established that the proposed tests are consistent, and the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enables us to compute the asymptotic power of these tests. Furthermore, it is observed that the computations associated with the proposed tests are unburdensome. Besides, these tests perform better than many other tests available in the literature when data are generated from various distributions such as heavy-tailed distributions, which indicates that the proposed methodology is robust as well. Finally, the usefulness of the proposed graphical toolkit and tests is shown on two benchmark real data sets. This is a joint work with Pratim Guha Niyogi (Johns Hopkins University, USA). 

Analysis Seminar: Annual Progress Seminar
Thursday,  15 February, 3.30 pm
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Venue: Room 215

Host: Sourav Pal

Speaker: Priyanka Aroda
Affiliation: IIT Bombay

Title: Geometric and function theoretic aspects of the tetrablock
Abstract: We study the tetrablock, a domain in \mathbb{C}^3 given by 

\mathbb{E}=\left\{\left(x_1,x_2,x_3\right) \in \mathbb{C}^3 : \ 1-x_1 z-x_2 w+x_3 zw \neq 0 \ \ \text{for} \ \ |z| \leq 1,|w| \leq 1\right\}.\]The tetrablock is related to a certain function-theoretic problem that arises in control engineering. We discuss several characterizations for the elements in$\mathbb{E}$ and in its closure. We present a set of necessary and sufficient conditions that provide a Schwarz lemma for $\mathbb{E}$. We also describe the automorphism group of $\mathbb{E}$. 

Geometry and Number Theory seminar
Thursday, 15th February 2024, 4 pm-5 pm
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Venue: Ramanujan Hall
Host: K. Mallesham.

Speaker: Dr. Rahul Kumar Singh
Affiliation: IIT Patna

Title: Zero Mean Curvature Surfaces and Ramanujan's Identities

Abstract: In this talk, we discuss an interesting connection between examples of zero mean curvature surfaces in Euclidean and Lorentz-Minkowski 3-space and some special Ramanujan identities.

Topology and Related Topics Seminar

Thursday, 16 February  2023, 11:30-12:30

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Venue: Ramanujan hall

Host: Rekha Santhanam

Speaker: Sahin Mandal

Affiliation: IIT Bombay

Title: Quillen Q-Construction

Abstract: In this series of two talks we will define higher algebraic k 
theory using Quillen's Q construction.