January 2020
Public Access Category: All |

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

Speaker: Aaron Charles Naber.

Affiliation: Northwestern University.

Date and Time: Monday 06 January, 11:00 am - 12:00 noon.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Analysis of Geometric Nonlinear Partial Differential Equations.

Abstract: It is well known that solutions of a linear elliptic equation,

for instance a harmonic function $\Delta u = 0$, are automatically smooth.

Indeed, one has many ways to quantify this and understand precise

estimates on solutions. In the context of nonlinear equations, this need

not be the case and one may be forced to deal with a singular set

$Sing(u)$. Though dimension estimates on singular sets have been

understood since the 60's, it is only in the last few years that the

structure of the singular sets is starting to come into focus. This talk

will give an introduction to all of this, including a rough idea of the

methods and results. We will study the case of nonlinear harmonic maps as

it requires the least background, however these methods and extensions

have been used lately in many areas (e.g. minimal surfaces, Yang-Mills,

Einstein manifolds, nodal analysis and Q-valued harmonic maps, to name a

few).v

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. G01, Computer Center Conference Room.
- Description:
- Infosys Prize Lecture.

Speaker: Siddhartha Mishra.

Affiliation: ETH Zurich.

Date and Time: Wednesday 08 January, 02:30 pm - 03:30 pm.

Venue: Room No. G01, Computer Center Conference Room.

Title: How Do You Fathom Fluids? – A Statistical Perspective.

Abstract: The Euler equations were proposed more than 250 years ago to

model the flow of inviscid fluids. But their mathematical understanding is

far from complete even today and simulating them is a formidable

challenge. Prof. Mishra will talk about some recent developments in the

area of statistical solutions for analyzing and computing fluid flows,

modeled by the Euler equations.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminars.

Speaker: Dipendra Prasad.

Affiliation: IIT Bombay.

Date and Time of Lecture I: Friday 17 January, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Reflexive modules on quotient surface singularities and the McKay

correspondence.

Abstract: These two lectures will give an overview of MacKay

correspondence which relates (irreducible representations) of finite

subgroups G of SL(2,C), and (indecomposable) reflexive modules over

C[|X,Y|]^G. The first lecture will be of an introductory nature, talking

about finite subgroups of GL(n,C) in general, and singularity theory.

- Time:
- 11:45am
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra Seminars:

Speaker: Dilip Patil.

Affiliation: IISc, Bengaluru.

Date and Time: Tuesday 21 January, 11:45 am - 01:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Smooth morphisms and Jacobian criterion.

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

Speaker: S. Venkatesh.

Affiliation: Department of Mathematics, IIT Bombay.

Date and Time: Wednesday 22 January, 11:00 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Improved Bounds for the Sunflower Lemma.

Abstract: For a positive integer r, an r-sunflower is a collection of r

finite sets such that the intersection of any two sets is the intersection

of all. The Erdos-Rado Sunflower conjecture states that for any fixed

positive integer r, there exists a constant c>0 such that the following

holds for eventually all positive integers w: for every collection of at

least c^w sets, each having size w, there exists a subcollection which is

an r-sunflower.

Erdos and Rado (1960), while posing the Sunflower conjecture, showed that

every collection with at least about w^w sets, each having size w, will

contain an r-sunflower. In this talk, we will see an improvement by

Alweiss, Lovett, Wu and Zhang (2019), who show that every collection with

at least about (log w)^w sets, each having size w, will contain an

r-sunflower.

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Pratulananda Das.

Affiliation: Jadavpur University.

Date and Time: Wednesday 22 January, 02:30 pm - 03:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Characterized subgroups of the Circle.

Abstract: In this talk the history and the developments of the notion of

characterized subgroups of the circle group would be discussed along with

some of the main observations obtained over the years. This would be

followed by presentation of certain very recent developments in this area

carried out by using a more general method of convergence.

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

Speaker: Bata Krishna Das.

Affiliation: IIT Bombay.

Date and Time: Wednesday 22 January, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Model of operators and their characteristic functions.

Abstract:

Dilations of Hilbert space operators is a basic and useful tool which is used to understand non-normal operators. In this talk, we will discuss Sz.-Nagy’s unitary dilations of contractions and some of its far reaching consequences in function theory and operator theory. This inparticular will include a functional model for a class of contractions and their charac- teristic functions. If time permits we will also discuss a recently developed multivariate analogue of these notions.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra Seminars:

Speaker: Dilip Patil.

Affiliation: IISc, Bengaluru.

Date and Time: Friday 24 January, 03:30 pm - 05:00 pm

Venue: Room 215, Department of Mathematics.

Title: Smooth morphisms and Jacobian criterion.

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

Speaker: Marius Tucsnak.

Affiliation: Universite de Bordeaux.

Date and Time: Monday 27 January, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Mathematics and swimming of aquatic organisms.

Abstract: We pass in review recent results on the mathematical modelling

of solids in a viscous fluid. We discuss, in particular, questions

connected to the wellposedness and the qualitative behavior of solutions.

We finally emphasize the case of self-propelled motions , in connection

with the modelling of swimming of aquatic organisms.

- Time:
- 11:45am - 1:00pm
- Location:
- Room 113, Department of Mathematics
- Description:
- Commutative Algebra & Algebraic Geometry seminar.

Speaker: Rajendra Gurjar.

Affiliation: IIT Bombay.

Date and Time: Tuesday 28 January, 11:45 am - 1:00 pm.

Venue: Room 113, Department of Mathematics.

Title: Cyclic unramified coverings of varieties.

Abstract: We will show how cyclic unramified coverings of algebraic

varieties can be constructed using units in the coordinate ring of the

variety, or torsion divisor classes. Converse of this will also be

discussed. We will show how topology of the variety influences such

covers.

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

Speaker: Anand Sawant.

Affiliation: School of Mathematics, TIFR.

Date and Time: Wednesday 29 January, 04:00 pm - 05:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Central extensions of algebraic groups revisited.

Abstract: The study of central extensions of a group, which began with the

work of Schur, has a long history spanning more than a hundred years.

Celebrated results of Steinberg and Matsumoto obtained about fifty years

ago determine the universal central extension of certain algebraic groups.

These results have lead to a lot of interesting developments, for

instance, the work of Brylinski and Deligne about determining the category

of central extensions of a reductive group by K_2 in terms of certain

quadratic forms. I will briefly survey these classical results and discuss

how all these results can be uniformly explained and generalized using

motivic homotopy theory. The talk is based on joint work with Fabien Morel

and will not presume any knowledge of motivic homotopy theory.