Research Scholars' Seminar Series

Lecture Number: | 87 |

Title: | Introduction to Bifurcation Theory |

Speaker: | Devanand |

Date: | 15th September 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this talk I will give some mathematical background which is required for introducing bifurcation. Further I will discuss some basic types of bifurcation with the help of example.

Lecture Number: | 86 |

Title: | Mathematical Modelling on Drug Transport Phenomena |

Speaker: | Koyel Chakravarty |

Date: | 1st September 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: Of concern the present theoretical investigation on the administration of drug in various tissues of the living systems through the appropriate choice of mathematical modelling is to understand and to estimate the drug kinetics. The concept of the administration of drug in tissues under various situations may appear simplistic, but such penetration of drug in these tissues regulates the clinical effectiveness and toxic potential of antibacterial agents and other drugs. The complete knowledge of tissue distribution principles is necessary in order to compare the therapeutic action of various drugs and antibacterial agents. The primary objective of the study is to show how mathematical models play significant role in pharmacokinetics for transportation of drugs in various tissues and its clinical implications.

Lecture Number: | 85 |

Title: | An Example of Nowhere Differentiable Continuous Function |

Speaker: | Ranjan Kumar Das |

Date: | 18th August 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this talk we will discuss about nowhere differentiable continuous function. We will go through its history and then see an example.

Lecture Number: | 84 |

Title: | Finite element error analysis for parabolic problems |

Speaker: | Tanushree Ray |

Date: | 4th August 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this seminar, we will study the discretization of domain and the construction of finite element space. Then the apriori error estimates for parabolic problem in L^{2} norm and H^{1} norm will be presented.

Lecture Number: | 83 |

Title: | Heisenberg uniqueness pairs for the Fourier transform |

Speaker: | Deb Kumar Giri |

Date: | 24th April 2015 (Friday) |

Time: | 1100-1200 |

Abstract: In general, Heisenberg uniqueness pair is a variance of uncertainty principle for the Fourier transform. Heisenberg uniqueness pair (HUP) is a question of dealing with the uniqueness property of finite Borel measure which is supported on a curve whose Fourier transform vanishes on a set.

In 2011, H. Hedenmalm and A. M. RodrÃez had shown that (hyperbola, some discrete set) is a HUP. There after, a considerable amount of work has been done for HUP in the plane as well as in the Euclidean spaces

In this talk, Mr. Giri will indicate the work so far done by others as well as some of our recent observations.

Lecture Number: | 82 |

Title: | An Introduction to Free Groups |

Speaker: | Ramesh Prasad Panda |

Date: | 21st April 2015 (Tuessay) |

Time: | 1530-1630 |

Abstract: Finding structure of a Group involves listing of its generators & determining the relations between them. One can study the formal background of this concept with the help of Free Groups. In this talk, I will begin with construction & definition of Free Groups. Then I will state & prove Universal Mapping Property of Free Groups which leads to definition of a Group in terms of Generators & Relations. Finally, I will talk about some applications of Free Groups.

Lecture Number: | 81 |

Title: | Existence and Uniqueness of the finite element solution of a nonlinear parabolic problem |

Speaker: | Pratibha Shakya |

Date: | 31st March 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this seminar, an existence and uniqueness of the finite element solution of a nonlinear parabolic problem will be discussed. Existence and uniqueness will be proved by using appropriate assumption on the source function and the nonlinear coefficient. We will conclude this seminar by presenting some error estimates for the semidiscrete scheme for the problem.

Lecture Number: | 80 |

Title: | Existence of Algebraic Closure of a field: Artin's proof |

Speaker: | Ayan Sengupta |

Date: | 17th March 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: There are several proofs of existence of algebraic closure of any arbitrary field.In this seminar we will see one particular proof (more suitably, construction) based on Zorn's lemma.This proof was constructed by Emil Artin.We will also prove the uniqueness of algebraic closure (up to isomorphism).

Lecture Number: | 79 |

Title: | Simplicity of Projective Special Linear Group |

Speaker: | Ashish Kesarwany |

Date: | 3rd March 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: I am going to give talk about Simplicity of Projective Special Linear Groups. For this, firstly I shall dene what is projective linear groups and special projective linear groups. Then I shall state and prove the Iwasawa's criterion and nally using the iwasawa's theorem I will prove the simplicity of PSL(n,F).

Lecture Number: | 78 |

Title: | On the Language of Primitive Partial Words |

Speaker: | Ananda Chandra Nayak |

Date: | 17th February 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: A partial word is a word which contains some holes known as do not know symbols and such places can be replaced by any letter from the underlying alphabet. We study the relation between language of primitive partial words with the conventional language classes viz. regular, linear and deterministic context-free in Chomsky hierarchy. We give proofs to show that the language of primitive partial words over an alphabet having at least two letters is not regular, not linear and not deterministic context free language. Also we give a 2DPDA automaton that recognizes the language of primitive partial words.

Lecture Number: | 77 |

Title: | A Fitted Operator Method for Singular Perturbation Problem |

Speaker: | Maneesh Kumar Singh |

Date: | 3rd February 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this talk I will discuss about Singular Perturbation Problem and there numerical solution. First I will discuss an example of Singular Perturbed diffenential equation with defining its boundary layer. And then I will discuss some classical difference scheme, why they do not work well after that A tted operator method for same problem.

Lecture Number: | 76 |

Title: | Complex Dynamics |

Speaker: | Madhusudan Bera |

Date: | 20th January 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this talk I will discuss basic Iteration Theory, properties of Fatou and Julia set and some of their characterisation. I also talk about periodic points of a function and their classification and singular values and classification of periodic Fatou Components.

Lecture Number: | 75 |

Title: | An explicit construction of innitely many quadratic fields of even class number from the rational points of elliptic curves of rank greater than equal to 1 |

Speaker: | Debopam Chakraborty |

Date: | 06th January 2015 (Tuesday) |

Time: | 1600-1700 |

Abstract: In this talk I will explicitly construct an infinite family of quadratic number fields of class number divisible by two. The main idea is to relate a certain class of rational points of an elliptic curve to a quadratic field whose class number will eventually be divisible by two.