March 18, 2024 - March 22, 2024
Public Access Category: All |
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- 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.