November 2019
Public Access Category: All |

- Time:
- 4:15pm - 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Mrinal Kumar.

Affiliation: Computer Science Department, IIT Bombay.

Date and Time: Friday 01 November, 4:15 pm - 5:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Polynomial Method in Combinatorics (Part III).

Abstract: Upper bounds on the size of 3-AP free sets over finite fields:

We will discuss a recent result of Ellenberg and Gijswijt who showed that

if F is a finite field with three elements, and S is a subset of of F^n

such that S does not that does not contain three elements in an

arithmetic progression, then |S| is upper bounded by c^n for a constant c

< 3.

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

Speaker: Dilip Patil.

Affiliation: IISc Bengaluru.

Date and Time: Monday 04 November, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Module of Kahler Differentials, smooth morphisms, Cohen Structure

Theorems.

Abstract:

(During the week 03 Nov – 08 Nov, 2019) We continue to study smooth morphisms. The

purpose of these two lectures is :

(1) Definitions and Basic properties of the Module of Käher differentials.

(2) Prove a criterion for when a quotient of a formally smooth algebra is again formally

smooth.

(3) Prove a characterisation of when a morphism is smooth called the J a c o b i a n c r i -

t e r i o n.

This is a preparation for the proof of Cohen’s structure theorem for complete local rings in

the inequicharacteritic case.

- Time:
- 5:00pm - 6:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Saurav Bhaumik.

Affiliation: IIT Bombay.

Date and Time: Monday 04 November, 5:00 pm - 6:30 pm.

Venue: Room 215, Department of Mathematics.

Title: Higgs bundles and the Hitchin fibration.

Abstract: We will introduce Higgs bundles on curves, discuss the Hitchin

fibration and its fibers in terms of spectral curves.

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

Speaker: Tony Puthenpurakal.

Affiliation: IIT Bombay.

Date and Time: Thursday 07 November, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: An application of triangulated categories to linkage of ideals.

Abstract: We define and give elementary properties of triangulated

categories. We also give an application of triangulated categories to

linkage theory in commutative algebra.

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

Speaker: Dilip Patil.

Affiliation: IISc Bengaluru.

Date and Time: Friday 08 November, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Module of Kahler Differentials, smooth morphisms, Cohen Structure

Theorems.

Abstract:

(During the week 03 Nov – 08 Nov, 2019) We continue to study smooth morphisms. The

purpose of these two lectures is :

(1) Definitions and Basic properties of the Module of Käher differentials.

(2) Prove a criterion for when a quotient of a formally smooth algebra is again formally

smooth.

(3) Prove a characterisation of when a morphism is smooth called the J a c o b i a n c r i -

t e r i o n.

This is a preparation for the proof of Cohen’s structure theorem for complete local rings in

the inequicharacteritic case.

- Time:
- 5:00pm - 6:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Geometry and Topology seminar.

Speaker: Saurav Bhaumik.

Affiliation: IIT Bombay.

Date and Time: Tuesday 12 November, 5:00 pm - 6:30 pm.

Venue: Room 215, Department of Mathematics.

Title: Higgs bundles and the Hitchin fibration - II.

Abstract: We will introduce Higgs bundles on curves, discuss the Hitchin

fibration and its fibers in terms of spectral curves.

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: Arnab Roy.

Affiliation: INRIA, Nancy.

Date and Time: Wednesday 13 November, 3:00 pm - 4:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Stabilization of a rigid body moving in a compressible viscous fluid.

Abstract: In this talk, we discuss the stabilization of a fluid-structure

interaction system of a viscous, compressible fluid and rigid ball in a

three dimension space with an external force acting on the ball produced

by a spring and a damper connecting the centre of the ball to a fixed

point $h_1$. We prove global-in-time existence result for this model under

the condition that the initial velocities are small and the center of mass

of the body is sufficiently near to $h_1$. In this scenario, we discuss

the asymptotic behaviour of the whole system.

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

Speaker: Chandranandan Gangopadhyay.

Affiliation: The Institute of Mathematical Sciences, Chennai.

Date and Time: Wednesday 13 November, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Quot schemes and Semistable Vector Bundles.

Abstract: Let C be a smooth projective curve over an algebraically closed

field k. Fix r, d ≥ 1. Let Q(r, d)

be the quot scheme parametrizing degree d torsion quotients of the trivial

vector bundle of rank r. Then we show that the universal

kernel bundle over C × Q(r, d) and its pushforward to Q(r, d) are stable

with respect to certain

natural ample bundles over C × Q(r, d) and Q(r, d) respectively.

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Trygve Johnsen.

Affiliation: The Artic University of Norway.

Date and time: Friday 15 November, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Greedy weights for codes and matroids.

Abstract: Greedy weights of linear codes measure the minimal support

cardinality

of chains of subcodes for a certain lexicographic order. We show how the

problem

of finding such weights can be studied by inspecting the poset of flats of

the generator matroid, or better: the (dual) poset of cycles for the

parity check matroid. The terms of a minimal resolution of the

Stanley-Reisner ring of the independence complex of the parity check

corresponds to the points of the poset. Optimal paths in the poset

diagram, and optimal chains of non-zero component maps in a minimal

resolution of the Stanley-Reisner ring. correspond to greedy weights Such

maps can be constructed using poset homology, or studied indirectly,

through the Taylor complex, which also provides a resolution, although

not minimal.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar (A discussion session).

Organisers: Trygve Johnsen and Madhusudan Manjunath.

Date and time: Monday 18 November, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Matroids, Coding Theory and Syzygies: A Discussion Session.

Abstract: We will discuss potential future directions in the interface

between matroids, coding theory and syzygies. This will be a platform to

share thoughts on this topic.

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

Speaker: Dinesh Thakur.

Affiliation: Rochester University.

Date and Time: Friday 22 November, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: What should pi, e, zeta(3), Gamma(1/7) be, if integers are replaced

by polynomials?

Abstract: In this talk, which should be accessible to all undergraduates,

we will explain the title, and explain how number theory understands

interesting numbers and relations between them by building appropriate

mathematical structures, from algebra, geometry, analysis.

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

Speaker: Jinhyun Park.

Affiliation: KAIST, Republic of Korea.

Date and Time: Thursday 28 November, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On motivic cohomology for schemes with singularities.

Abstract: On smooth k-schemes, it is known that the higher Chow groups of

S. Bloch give what is called the motivic cohomology theory on them. When

schemes admit singularities, this has been yet unresolved.

In this talk, I will give a sketch of a recent new construction, which

gives a functorial theory on the category of all schemes of finite type.

To motivate the audience, I will begin with basic motivating examples from

1st year graduate course level differential forms, and proceed to build up

on it to give a sketch, and discuss some consequences and questions.