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.