July 2019
Public Access Category: All |

- Time:
- 11:30am - 12:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Algebra Seminar

Speaker: Dr. Rabeya Basu.

Time and Date: 11:30-12:30pm, Tuesday 2 July.

Title: On transvection subgroups of classical groups.

Abstract: In this seminar we shall discuss the analogue of

Quillen-Suslin's local-global principle for the transvection subgroups of

the full automorphism groups, and its application to generalise results in

classical K-theory from the free modules to the projective modules.

- Time:
- 11:00am
- Location:
- Room No. 105, Department of Mathematics
- Description:
- Number Theory Seminar

Speaker: Saad Qadri, IIT Bombay.

Time and Date: 11:00 am, Thursday, July 04.

Venue: Room 105.

Title: The prime number theorem.

Abstract: Our goal is to give an outline of the proof of the prime number

theorem. Let π(x) be the prime-counting function that gives the

number of primes less than or equal to x. The prime number theorem then

states that π(x) is asymptotically equal to x/log x. The proof

involves application of the methods of complex analysis to the study of

the real valued function π(x).

- Time:
- 3:00pm - 4:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 1.

Speaker: Anisa Chorwadwala.

Affiliation: IISER Pune.

Date and Time: Wednesday 10 July, 3:00 pm - 4:00 pm.

Venue: Room 216, Department of Mathematics.

Title: A Glimpse of Shape Optimization Problems.

Abstract: The following questions arise quite naturally from what we see

around us. Why are soap bubbles that float in air approximately spherical?

Why does a herd of reindeer form a round shape when attacked by wolves? Of

all geometric objects having a certain property, which ones have the

greatest area or volume; and of all objects having a certain property,

which ones have the least perimeter or surface area? These problems have

been stimulating much mathematical thought. Mathematicians have been

trying to answer such questions and this has led to a branch of

mathematical analysis known as “shape optimisation problems”.

A typical shape optimisation problem is, as the name suggests, to find a

shape which is optimal in the sense that it minimises a certain cost

functional while satisfying given constraints. Isoperimetric problems form

a special class of shape optimisation problems. A typical isoperimetric

problem is to enclose a given area with a shortest possible curve. In

many cases, the functional being minimised depends on solution/s of a

given partial differential equation defined on a variable domain.

The plan is to give a glimpse of a few shape optimization problems we have

worked on.

- Time:
- 4:30pm - 5:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 2.

Speaker: Apala Majumdar.

Affiliation: University of Bath.

Date and Time: Wednesday 10 July, 4:30 pm - 5:30 pm.

Venue: Room 216, Department of Mathematics.

Title: Solution Landscapes in the Landau-de Gennes Theory for Nematic

Liquid Crystals.

Abstract: Nematic liquid crystals are quintessential examples of soft

matter, intermediate in character between solids and liquids, with

long-range orientational order. We model spatio-temporal pattern formation

for nematic liquid crystals on two-dimensional polygonal geometries, which

are relevant for applications. We work within the powerful continuum

Landau-de Gennes theory for nematic liquid crystals. We illustrate the

complex solution landscapes on square domains as a function of the square

size, temperature and boundary conditions, reporting a novel Well Order

Reconstruction Solution on nnao-scale geometries. We discuss

generalizations to arbitrary 2D polygons, using symmetry-based and

variational techniques to study stable patterns in distinguished

asymptotic limits. We conclude by reviewing recent work on stabilization

of interior vortices by magneto-nematic coupling in ferronematics, which

leads to new possibilities for magneto-mechanical effects in nematic-based

materials. This is joint work with researchers in Peking University,

Shanghai Jiao Tong, IIT Delhi, IIT Bombay, Illinois Technological

University and University of Verona.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Algebraic Geometry seminar.

Speaker: Mrinmoy Datta.

Affiliation: The Arctic University of Norway.

Date and Time: Thursday 11 July, 4:00 pm - 5:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Bounds on the number of rational points on hypersurfaces defined

over finite fields.

Abstract: In this talk, we will revisit some of the known bounds on the

number of rational points on hypersurfaces of a given degree defined over

a finite field. We will recall a conjecture proposed by Homma and Kim

towards a tight upper bound on the number of rational points on a

nonsingular hyperface contained in an even dimensional projective space

over a finite field. Finally, we will present a recent work towards

proving the above mentioned conjecture for nonsingular threefolds

contained in a four-dimensional projective space.

- Time:
- 11:00am
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Partial Differential Equations seminar.

Speaker: Sheetal Dharmatti.

Affiliation: IISER Thiruvananthapuram.

Date and Time: Friday 12 July, 11:00 am - 12:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Data assimilation type Optimal control problem for Cahn Hilliard

Navier Stokes' system.

Abstract: This work is concerned about some optimal control problems

associated to the evolution of two isothermal, incompressible, immiscible

fluids in a two-dimensional bounded domain. The

Cahn-Hilliard-Navier-Stokes model consists of a Navier亡tokes equation

governing the fluid velocity field coupled with a convective Cahn蓬illiard

equation for the relative concentration of one of the fluids. A

distributed optimal control problem is formulated as the minimization of a

cost functional subject to the controlled nonlocal

Cahn-Hilliard-Navier-Stokes equations. We establish the first-order

necessary conditions of optimality by proving the Pontryagin maximum

principle for optimal control of such system via the seminal Ekeland

variational principle. The optimal control is characterized using the

adjoint variable. We also study another control problem which is similar

to that of data assimilation problems in meteorology of obtaining unknown

initial data using optimal control techniques when the underlying system

is same as above.

- Time:
- 12:00pm - 1:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Partial Differential Equations seminar

Speaker: Utpal Manna.

Affiliation: IISER Thiruvananthapuram.

Date and Time: Friday 12 July, 12:00 pm - 1:00 pm.

Venue: Room 216, Department of Mathematics.

Title: Weak Solutions of a Stochastic Landau豊ifshitz萌ilbert Equation

Driven by Pure Jump Noise.

Abstract: In this work we study a stochastic three-dimensional

Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the

Marcus canonical form. We show existence of weak martingale solutions

taking values in a two-dimensional sphere $S^2$ and discuss certain

regularity results. The construction of the solution is based on the

classical Faedo-Galerkin approximation, the compactness method and the

Jakubowski version of the Skorokhod Theorem for nonmetric spaces. This is

a joint work with Zdzislaw Brzezniak (University of York) and has been

published in Commun. Math. Phys. (2019),

https://doi.org/10.1007/s00220-019-03359-x.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Probability and Statistics Seminar.

Speaker: K.B. Athreya.

Affiliation: Iowa State University.

Date and Time: Friday 26 July, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: What can you do with one uniform random variable?

Abstract: Given one uniform(0,1) random variable we show that one can

generate a sequence of iid uniform r.v. and give some applications.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Title: On a question of Suslin about completion of unimodular rows

Abstract:

R.G. Swan and J. Towber showed that if (a2, b, c) is a unimodular row

over any commutative ring R then it can be completed to an invertible

matrix over R. This was strikingly generalised by A.A. Suslin who showed

that if (a

r!

0 , a1, . . . , ar) is a unimodular row over R then it can be com-

pleted to an invertible matrix. As a consequence A.A. Suslin proceeds to

conclude that if 1

r! ∈ R, then a unimodular row v(X) ∈ Umr+1(R[X])

of degree one, with v(0) = (1, 0, . . . , 0), is completable to an invertible

matrix. Then he asked

(Sr(R)): Let R be a local ring such that r! ∈ GL1(R), and let p =

(f0(X), . . . , fr(X)) ∈ Umr+1(R[X]) with p(0) = e1(= (1, 0, . . . , 0)). Is it

possible to embed the row p in an invertible matrix?

Due to Suslin, one knows answer to this question when r = d + 1,

without the assumption r! ∈ GL1(R). In 1988, Ravi Rao answered this

question in the case when r = d.

In this talk we will discuss about the Suslin’s question Sr(R) when r =

d − 1. We will also discuss about two important ingredients; “homotopy

and commutativity principle” and “absence of torsion in Umd+1(R[X])

Ed+1(R[X]) ”,

to answer Suslin’s question in the case when r = d − 1, where d is the

dimension of the ring.