4pm» Deepkumar Makadiya, IIT Bombay- 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. GargeTitle: 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