- Time:
- 4:00pm
- Location:
- Room No. 105, Department of Mathematics
- Description:
**Algebraic Groups seminar****Date**Friday, 1st March, 4 pm

**Venue**Room 105

**Host**Dipendra Prasad

**speaker**Deep Makadiya

**Affiliation****IIT Bombay****Title**Regular elements of semi-simple algebraic groups

**Abstract:**We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on 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

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Analysis seminar****Date**Friday, 1 Mar, 4 pm

**Venue**Ramanujan Hall

**Host**Saikat Mazumdar

**speaker**Saikat Mazumdar

**Affiliation****IIT Bombay****Title**Taming explosions by blowing up

**Abstract:**In this talk, I will consider the question of compactness of (approximate) solutions to some Yamabe-type problems. We will see that by appropriately blowing up the singularities a finer analysis often reveals some analytical or geometric rigidity, thereby ruling out explosions. This establishes uniform bounds which implies compactness (in the appropriate topology) and gives existence and non-existence results.

- Time:
- 11:30am - 12:30pm
- Location:
- Room 215, Mathematics Department
- Description:
**Topology and Related Topics Seminar****Date**Tuesday, 5 March 2024, 11:30-12:30 pm

**Venue****Room 215****Host**Rekha Santhanam

**speaker**Sahin Mandal

**Affiliation**IIT Bombay

**Title**Quillen Q-construction

**Abstract**In the second talk

**,**we will define higher algebraic k theory using Quillen’s Q construction.

- Time:
- 4:00pm - 5:00pm
- Description:
**Commutative Algebra****Seminar****Date**Tuesday, 05 Mar, 4 pm—5 pm

**Venue**Room 215

**Host**Tony J. Puthenpurakal

**speaker**Omkar Javadekar

**Affiliation**IIT Bombay

**Title**A theorem of Bruns on free resolutions of ideals generated by three elements

**Abstract**Let

*R*be a commutative Noetherian ring. In 1972, P. Cohn proved that for every finitely generated*R*-module*M*, there exists a three-generated ideal*I*of*R*such that pd(*M*)=pd(*R/I*). In this series of two talks, we will see a generalization of Cohn's result due to W. Bruns. We will show that "every" finite free resolution over*R*is a free resolution of a 3-generated ideal of*R*.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups Seminar****Date**Tuesday, March 5, 2024, 4 pm

**Venue**Ramanujan Hall

**Host**Shripad M. Garge

**speakers**Shripad M. Garge

**Affiliation**IIT Bombay, Mumbai

**Title**Semi-simple automorphisms

**Abstract**We study some inner automorphisms of algebraic groups.

- Time:
- 4:00pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics colloquium****https://www.math.iitb.ac.in/NewsEvents/IIT_Bombay_Talk_Grothendieck_Leila_Schneps_Pierre_Lochak.pdfColloquim about Grothendieck's life and works****Date**Wednesday, March 6th, 4 pm-6 pm**Venue**Room number 23, VMCC**Host**Dipendra Prasad**speakers**Leila Schneps and Pierre Lochak**Affiliation**Institut de Mathématiques de Jussieu, Paris**Title**Alexander Grothendieck: his life, his mathematics, and his writings.**Abstract**Alexander Grothendieck was arguably the most original, influential, and the most prolific mathematician of the 20th century. After retiring from active mathematics in his early 40's, he contributed to several newer fundamental insights. This lecture will reflect on some of the enigmas around him, before and after “retirement".

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**PDE and analysis seminar****Date**Thursday, March 7, 4 pm - 5 pm

**Venue**Ramanujan Hall

**Host**Chandan Biswas

**speaker**Dhriti Ranjan Dolai

**Affiliation**IIT Dharwad

**Title**The central limit theorem (CLT) for integrated density of states (IDS) of discrete random Schrodinger operator (Anderson model on lattice)

**Abstract**First, we will define the random Schrodinger operator on the Hilbert space of square summable functions on the d-dimensional integer lattice, and discuss its spectral properties. Also, we will talk about the integrated density of states (IDS). Now, we will consider the existence of the integrated density of states (IDS) as analogous to the law of large numbers (LLN). Then, we will prove the analogous central limit theorem (CLT) when test functions are either polynomials or first-order differentiable with polynomial growth.

- Time:
- 5:15pm - 6:45pm
- Location:
- Room 215, Mathematics Department
- Description:
**Algebraic Groups seminar****Date**Thursday, 7 March, 5.15-6.45

**Venue**Room 215

**Host**Dipendra Prasad

**speakers**Dibyendu Biswas

**Affiliation**IIT Bombay

**Title**Regular elements of semi-simple algebraic groups

**Abstract**We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on 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

- Time:
- 11:30am
- Location:
- Room 215, Mathematics Department
- Description:
**Algebraic Geometry Seminar****Date**Tuesday, 12 March, 11.30 am

**Venue**Room 215

**Host**Sudarshan Gurjar

**speaker**Nitin Nitsure

**Affiliation**Bhaskaracharya Pratishthana

**Title**Galois descent, twisted forms, and Galois cohomology.

**Abstract**We will first briefly recall faithfully flat descent (which was done in detail in the previous talk), and the geometry of finite Galois covers and their fiber powers (which was done in detail earlier). Then we will translate faithfully flat descent into Galois covering terms, to arrive at a formulation of descent and effective descent purely in terms of Galois groups and their actions. We will then show how to parameterize twisted forms of various structures via the first Galois cohomology. We will illustrate everything with examples from algebra and algebraic geometry. Finally, we will address the question of effective Galois descent for schemes.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic groups seminar**Date

Tuesday, 12 March, 4 pm

Venue

Ramanujan Hall

**Host**Shripad Garge

**speaker**Akash Yadav

**Affiliation**IIT Bombay

**Title**Complete varieties I

**Abstract**We introduce the notion of complete varieties to study parabolic subgroups of linear algebraic groups.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room 215, Mathematics Department
- Description:
**Commutative Algebra Seminar****Date**Tuesday, 12 Mar, 4 pm—5 pm

**Venue**Room 215

**Host**Tony J. Puthenpurakal

**speaker**Omkar Javadekar

**Affiliation**IIT Bombay

**Title**A theorem of Bruns on free resolutions of ideals generated by three elements-II

**Abstract**Let R be a commutative Noetherian ring. In 1972, P. Cohn proved that for every finitely generated R-module M, there exists a three-generated ideal I of R such that pdim(M)=pdim(R/I). In this series of two talks, we will see a generalization of Cohn's result due to W. Bruns. We will show that "every" finite free resolution over R is a free resolution of a three-generated ideal of R.

- Time:
- 11:30am - 12:30pm
- Description:
**Topology and Related Topics Seminar****Date**Friday, 15 March 2024, 11:30-12:30 pm

**Venue**Room 215

**Host**Rekha Santhanam

**speaker**Sahin Mandal

**Affiliation**IIT Bombay

**Title**Quillen Q-construction-II

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups Seminar**Friday, 15 March, 2024, 2.30 pm

====================

**Venue:**Ramanujan Hall**Speaker:**Sulakhana Chowdhury**Affiliation:**IISER Thiruvananthapuram

**Host:**Shripad M. Garge**Title:**Permutation modules of the walled Brauer algebras

**Abstract:**In this talk, we will discuss the permutation modules and Young modules of the group algebras of the direct product of symmetric groups and the walled Brauer algebras. In the category of dual Specht-filtered modules, if the characteristic of the field is neither 2 nor 3, then the permutation modules are dual Specht-filtered, and the Young modules are relative projective cover of the dual Specht modules. We prove that the restrictions of the cell modules of the walled Brauer algebras to the group algebras of the direct product of the symmetric groups are dual Specht filtered, and the Young modules act as the relative projective cover of the cell modules of the walled Brauer algebras. Finally, we prove that if char K differs from 2 and 3, the permutation modules can be written as a direct sum of indecomposable Young modules.

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No 105, Department of Mathematics
- Description:
**Algebraic groups seminar****Date**Friday, 15 March, 4 pm-5.30 pm

**Venue**Room 105

**Host**Dipendra Prasad

**speaker**Mohammad Saad

**Affiliation**IIT Bombay

**Title**Regular elements of semi-simple algebraic groups

**Abstract**We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on 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

- Time:
- 5:00pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Time:
- 11:30am
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Algebraic Geometry Seminar****Date**Tuesday, 19 March, 11.30 am

**Venue**Room 215

**Host**Sudarshan Gurjar

**speaker**Nitin Nitsure

**Affiliation**Bhaskaracharya Pratishthana

**Title**Effective Galois descent for Schemes and Algebraic Space.

**Abstract**We will translate faithfully flat descent and effective descent into Galois theoretic terms, and give examples. Then we will consider the problem of effective Galois descent for the fibered categories of schemes and algebraic spaces. While effective Galois (and etale) descent holds for algebraic spaces, we will give an elementary example showing it does not hold for the subcategory of algebraic spaces formed by schemes. This is one of the advantages of generalizing from schemes to algebraic spaces.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic Groups Seminar

Tuesday, March 19, 2024, 4 pm====================

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Akash Yadav

Affiliation: IIT Bombay, Mumbai

Title: Parabolic subgroups IAbstract: We introduce the notion of parabolic subgroups in linear algebraic groups.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:

**Commutative Algebra and Algebraic Geometry Seminar****Date**Tuesday, 19 March 2024, 4-5 pm

**Venue**Room 215

**Host**Tony J. Puthenpurakal

**speaker**R. V. Gurjar

**Affiliation**IIT Bombay

**Title**Some more results about Brieskorn-Pham singularities

**Abstract**We will discuss the following results. (1) Classification of 3-dimensional factorial B-P singularities by U.Storch. (2) Classification of affine B-P 3-folds which admit a non-trivial action of the additive group G_a (equivalently, a non-zero locally nilpotent derivation on their coordinate ring) by M. Chitayat. (3) Classification of affine B-P 3-folds which are rational (i.e. their function field is a purely transcendental extension of the ground field) by M Chitayat.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium****Date**Wednesday, 20 March, 4-5 pm

**Venue**Ramanujan Hall

**Host**Jugal Verma

**speaker**Nitin Nitsure

**Affiliation**Bhaskaracharya Pratishthana, Pune

**Title**Curvature and driving a car

**Abstract**The topic of this lecture is the differential geometry and topology of surfaces in the 3-dimensional Euclidean space. But my approach will be via the common experience of driving or traveling in a car or in an auto-rickshaw. Our everyday exposure to going along the curving roads and the up and down slopes in Powai gives us powerful tools to understand the concepts of curvature of curves on a surface, and also the Gaussian curvature of the surface itself, which involves looking up vertically from the sun-roof of the car, and doing a certain book-keeping! The experience of lurching sideways while driving up or down ramps gives the alternative view of Gaussian curvature as the product of principal curvatures. I will then give a pictorial proof of the Gauss-Bonnet theorem. The last topic will be my result (proved in 2019) on the determination of the curvature tensor of a higher dimensional Riemannian manifold via quadrilateral gaps, which arose from a question by Rajaram Nityananda for surfaces. In particular, this gives a very simple formula for Gaussian curvature in terms of driving a car.

The lecture will be mostly understandable to first-year undergraduate students. No formal background in differential geometry will be assumed. The emphasis will be on pictorial understanding rather than on epsilon-delta rigor.

- Time:
- 10:00am
- Location:
- Online Seminar meet.google.com/ooq-mzpy-tvk
- Description:
**Topology and Related Topics Seminar****Date**Friday, 22nd March 2024, 10:00 am

**Venue**Online Seminar meet.google.com/ooq-mzpy-tvk

**Host**Rekha Santhanam

**speaker**Ekansh Jauhari,

**Affiliation**University of Florida.

**Title**A new version of topological complexity and LS-category.

**Abstract**The topological Complexity (TC) of a topological space X is the minimal degree of instability of motion planning algorithms for autonomous systems with configuration space X. In this talk, we'll see a new version of TC, denoted as dTC, which seems to fit better for motion planning for some advanced autonomous systems. Like TC, our new version dTC also turns out to be a homotopy invariant. Moreover, dTC has a corresponding homotopy-invariant analog, denoted as dcat, to the Lusternik-Schnirelmann category (cat). We'll also see some interesting computations for both dTC(X) and dcat(X) for various nice spaces X as well as compare them with TC(X) and cat(X). (Based on joint work with Dr. Alexander Dranishnikov)

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No. 105, Department of Mathematics
- Description:
- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:

**Analysis seminar****Date**Friday, March 22, 4.30-5.30

**Venue**Ramanujan Hall

**Host**Chandan Biswas

**speaker**Niranjan Balchandran

**Affiliation**IIT Bombay

**Title**What is the Polynomial method-II?

**Abstract**We will discuss the Szemeredi-Trotter theorem.

- Time:
- 11:30am
- Description:
**Algebraic geometry seminar****Date**Tuesday, 26 March, 11.30 am

**Venue**Room 215

**Host**Sudarshan Gurjar

**speaker**Nitin Nitsure

**Affiliation**Bhaskaracharya Pratishthana

**Title**Galois descent and Galois cohomology: examples and calculations.

**Abstract**We will begin by recalling the calculus of Galois descent, and its translation into Galois cohomology classes for twisted forms. After that, we will look at common examples, involving Galois twisted forms of algebraic groups, Brauer Severi varieties, and vector bundles (Hilbert 90). The final example will be the Galois twisted from over reals of a non-separated affine line with doubled origin. This twisted form is an algebraic space which is not a scheme.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Topology and Related Topics Seminar****Date**Tuesday 26 March, 2:30 pm

**Venue**Ramanujan Hall

**Host**Rekha Santhanam

**speaker**Sudarshan Gurjar

**Affiliation**IIT Bombay

**Title**Vector bundles and Characteristic Classes

**Abstract**This is the second talk in the series of three talks. We will give an introduction to the characteristic classes of a vector bundle. Characteristic classes are invariants of a vector bundle taking values in the singular cohomology of the base and satisfying the obvious functoriality property with respect to pullback. They are the measure of the non-triviality of the vector bundle.

**The background assumed will depend on the audience present.**

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar****Date**Tuesday, 26 March 2024, 4-5 pm

**Venue**Room 215

**Host**Tony J. Puthenpurakal

**speaker**R. V. Gurjar

**Affiliation**IIT Bombay

**Title**Some more results about Brieskorn-Pham singularities-II

We will discuss the following results. (1) Classification of 3-dimensional factorial B-P singularities by U.Storch. (2) Classification of affine B-P 3-folds which admit a non-trivial action of the additive group G_a (equivalently, a non-zero locally nilpotent derivation on their coordinate ring) by M. Chitayat. (3) Classification of affine B-P 3-folds which are rational (i.e. their function field is a purely transcendental extension of the ground field) by M Chitayat.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Groups Seminar****Date**Thursday, March 28, 11 am

**Venue**Ramanujan Hall

**Host**Shripad M. Garge

**speaker**Akash Yadav

**Affiliation**IIT Bombay

**Title**Borel subgroups

**Abstract**We prove Borel's fixed theorem and introduce Borel subgroups.

- Time:
- 4:00pm - 5:30pm
- Location:
- Room No. 105, Department of Mathematics
- Description:
**Algebraic groups seminar****Date**Thursday, 28 March, 4 pm-5.30 pm

**Venue**Room 105

**Host**Dipendra Prasad

**speaker**Deep Makadiya

**Affiliation**IIT Bombay

**Title**Regular elements of semi-simple algebraic groups

**Abstract**We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on 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