March 2020
Public Access Category: All |

- Time:
- 5:15pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Nitin Nitsure.

Date and Time: Monday 02 March, 05:15 pm - 06:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Cotangent complex and applications -- Lecture No. 2.

Abstract: Differential 1-forms are very useful in the study of

multivariate calculus or smooth manifolds. Algebraically, the module of

Kahler differentials is very useful in commutative algebra. When the

spaces (or varieties) are not smooth but have singularities, differential

1-forms are not enough. Instead there is available a more general gadget

called the cotangent complex in commutative algebra as well as in

algebraic geometry. This series of talks will begin by recalling usual

differential forms and Kahler differentials in familiar setting, and then

introduce the cotangent complex. Applications to smoothness, local

complete intersections and deformation theory will be shown. Some

familiarity with the language of commutative algebra will be assumed.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: Manoj Kumar Keshari.

Affiliation: IIT Bombay.

Date and Time: Tuesday 03 March, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Tsen-Lang Theory of $C_i$-fields.

Abstract: We will define $C_i$-fields and prove results about algebraic

and transcendental extensions of such fields.

- Time:
- 2:15pm - 3:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Harsha Hutridurga.

Affiliation: IIT Bombay.

Seminar I.

Date and Time: Tuesday 03 March, 02:15 pm - 03:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On the Korn's inequality.

Abstract: Korn's inequality plays a fundamental role in elasticity theory

and also in hydrodynamics. This talk will aim at presenting the Korn's

inequality and some interesting observations around it. Furthermore, this

talk will some preliminary material for Friday's talk on 'Perturbative

analysis in linear elasticity'.

- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics seminar.

Speaker: Subhajit Ghosh.

Affiliation: IISc Bengaluru.

Date and Time: Wednesday 04 March, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Total variation cutoff for the flip-transpose top with random shuffle.

Abstract:

Abstract. We consider a random walk on the hyperoctahedral

group Bn generated by the signed permutations of the forms (i, n)

and (−i, n) for 1 ≤ i ≤ n. We call this the flip-transpose top

with random shuffle on Bn. We find the spectrum of the transition

probability matrix for this shuffle. We obtain the sharp mixing

time for this shuffle by proving total variation cutoff phenomenon

with cutoff time n log n.

- Time:
- 2:00pm - 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Analysis seminar.

Speaker: Bata Krishna Das.

Affiliation: IIT Bombay.

Date and Time: Wednesday 04 March, 02:00 pm - 03:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Model of operators and their characteristic functions.

Abstract: In this talk, using Sz.-Nagy and Foias isometric dilation, we will de-scribe functional models of a class of operators. This will further lead us to define their characteristic functions which are complete unitary in- variants. We will also discuss the connection between invariant subspace problem and factorization of characteristic functions. If time permits we will see a recently developed multivariate analogue of these notions.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Siddhartha Bhattacharya.

Affiliation: TIFR Mumbai.

Date and Time: Wednesday 04 March, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Translational tilings of the plane.

Abstract: A set $A\subset {\mathbb R}^2$ is said to be a translational

tile if ${\mathbb R}^2$ can be expressed as a disjoint union of

translated copies of $A$. In this talk we will discuss the connection

between such tiles and measure preserving dynamical systems. We will show

that if the underlying set $A$ satisfies a certain regularity condition

then the question whether $A$ tiles the plane is decidable.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:

Algebraic geometry seminar.

Speaker: Arjun Paul.

Affiliation: IIT Bombay.

Date and Time: Friday 06 March, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Mehta-Ramanathan's restriction theorems and their applications.

Abstract: Fundamental groups of algebraic varieties and their

representations are very interesting objects, and have given rise to a lot

of mathematics. The famous Narasimhan-Seshadri Theorem states that on a

compact Riemann surface there is a bijective correspondence between stable

holomorphic vector bundles with vanishing Chern classes and unitary

representations of the topological fundamental group. This result was

generalized to smooth projective surfaces by Donaldson. The Stable

Restriction Theorem of Mehta-Ramanathan then enables us to generalize this

correspondence, between stable holomorphic vector bundles with vanishing

Chern classes and unitary representations of the fundamental group, to

arbitrary smooth projective varieties. This consequence is the main

application we have in mind. We will also give an overview of the proof of

the Stable and Semi-stable Restriction theorems.

- Time:
- 2:15pm - 3:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Seminar II.

Speaker: Harsha Hutridurga.

Affiliation: IIT Bombay.

Date and Time: Friday 06 March, 02:15 pm - 03:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Perturbative analysis in linear elasticity.

Abstract: In this talk, we aim to answer the following question: How does

the traction-to-displacement map change with respect to small volume

perturbation of elasticity parameters in a given medium. using some

elementary tools and building upon an idea of Friedman and Vogelius, we

demonstrate that the boundary measurements deviate only a little as long

as the defects are of small volume and more importantly, irrespective of

the elasticity properties of the defect.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Poornima.

Affiliation: IIT Bombay.

Date and Time: Friday 06 March, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Elliptic Curves over the complex numbers and their uniformization.

Abstract: This talk will be a gentle introduction to elliptic curves. We

start with the algebraic definition of elliptic curves and then explain

uniformization of complex elliptic curves, i.e. realise each of them as a

quotient of the complex number by a lattice.

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
- Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Wednesday 11 March, 02:30 pm - 03:45 pm.

Venue: Room 113, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE V.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Swarnendu Sil.

Affiliation: ETH Zurich.

Date and Time: Wednesday 11 March, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Approximation questions in higher dimensional gauge theory.

Abstract: Although Yang-Mills functional and gauge theory originated in physics, its Riemannian or elliptic version has already influenced a vast territory of mathematics as a whole, ranging from real and complex differential geometry and differential topology of vector and principal bundles over manifolds to symplectic geometry and topology and even complex algebraic geometry. Nearly all of these spectacular developments followed our improved understanding of gauge theory over four manifolds. However, very little is known about gauge theory on manifolds of dimension five and higher. In this talk, we shall visit some of the major open questions in higher dimensional gauge theory and their connections to other branches of mathematics. We shall see why in this setting, we are forced to work with certain ‘weak’ notions of principal bundles and connections. Finally, we shall discuss how approximation questions, i.e. understanding when these weak classes of bundles and connections can be approximated by smooth bundles and connections, enters the fray and present a few recent results in this direction.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Nitin Nitsure.

Affiliation: IIT Bombay (visitor).

Date and Time: Thursday 12 March, 11:30 am - 01:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Cotangent Complex.

Abstract: Prof. Nitsure will continue his course of lectures on the

Cotangent Complex.

- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Arjun Paul.

Affiliation: IIT Bombay.

Date and Time: Friday 13 March, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Mehta-Ramanathan's restriction theorems and their applications - 2.

Abstract: This will be the second talk in this series.

- Time:
- 12:00pm - 1:00pm
- Location:
- Room No 215 Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: Swarnendu Sil.

Affiliation: ETH Zurich.

Date and Time: Friday 13 March, 12.00 noon - 01.00 pm.

Venue: Room 215, Department of Mathematics.

Title: Approximation of Sobolev bundles

Abstract: In this talk, I shall be focusing on the analytical issues

related to approximation of bundles and connections. I shall give an

overview of the analytical difficulties involved and how one can

circumvent those difficulties.

- Time:
- 2:00pm - 3:15pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Speaker: M. Vanninathan.

Affiliation: IIT Bombay.

Date and Time: Friday 13 March, 02:00 pm - 03:15 pm.

Venue: Room 114, Department of Mathematics.

Title: Asymptotic solutions of Hyperbolic PDE VI.

Abstract: We discuss several aspects of asymptotic solutions to some

models of Hyperbolic PDE with small wave lengths including their

construction and their justification. Necessary tools to carry out these

tasks will be introduced.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Dipendra Prasad.

Affiliation: IIT Bombay.

Date and Time: Friday 13 March, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: An Introduction to Bruhat-Tits Trees.

Abstract: This talk will be an introduction to Bruhat-Tits trees and their

applications.