Departmental Seminars:

Upcoming Talks:

 

No talks scheduled as of now.

 

Regular timing for seminar: 4 PM, Thursday.

Venue: Gallery II, Academic Complex, IIT Guwahati.

 

You can have a look at the upcoming seminar talks as well as at the talks that we have organized over the years, under the name IITG Mathematics Seminar Series. Please follow the link below to know about all the lectures that have taken place.

 

2006  2005  2004   2003       2002      2001     2000    1999     1998    1997    1996

 

IITG Mathematics Seminar Series came into being on 6th March 1996 with the inaugural lecture fittingly delivered by Prof Jyotiprasad Medhi, definitely the best mathematician in northeast India and a person respected all over the globe by Mathematics community.

 

To mark the completion of 100 talks of IITG Mathematics Seminar Series, Mathematics Day was celebrated with a full day programme on 21st August 2004, which also coincides with the birthday of the famous mathematician Augustin Louis Cauchy. Prof. Pradip Niyogi (Retd. Professor, IIT Kharagpur) and Prof. Kalyan B. Sinha (Director, ISI, Kolkata) delivered the 99th and 100th talks respectively.

 

Special lectures 125 and 126 by two eminent mathematicians were arranged to mark the completion of ten years of IITG Mathematics Seminar Series on 8h March 2006. Professor C.S. Seshadri of Chennai Mathematical Institute, Chennai and Professor Swadhin Pattanayak, Institute of Mathematics and Applications, Bhubaneswar delivered those lectures.

 

Current Convener:  Natesan Srinivasan

Past Conveners: Meenaxi Bhattacharjee, Swaroop Nandan Bora, Durga Charan Dalal, Arindam Sengupta, Bhaba Kumar Sarma

 

Talks held recently:

 

Lecture 167 (March 13, 2008) Delay-induced model for tumor–immune interaction and control of malignant tumor growth

By Dr. Sandip Banerjee, Birla Institute of Technology and Sciences (BITS), Pilani, Rajasthan.

(Abstract: The talk is based on the qualitative analysis of the solutions of a system of delay differential equations describing the competition between tumor and immune cells. The asymptotic stability of the possible steady states is showed and the occurrence of limit cycle of the system around the interior equilibrium is proved by the application of Hopf bifurcation theorem by using discrete time delay as a parameter of bifurcation. The length of the delay parameter for preserving stability of the system is also estimated, which gives the idea about the mode of action for controlling oscillations in malignant tumor cell growth. The theoretical and numerical outcomes have been supported through experimental results from literatures. This approach gives new insight of modeling tumor–immune interactions and provides significant control strategies to overcome the oscillations in tumor cells.)

 

Lecture 166 (February 7, 2008) Boundary value problem in nonlinear solid Mechanics and its finite element  implementation

By Dr. Arbind Kumar Singh, Department of Civil Engineering, IIT Guwahati.

(Abstract: The talk discusses the complexity associated with the mathematical models in nonlinear solid mechanics. Finite element methods and finite difference methods are widely used to solve these problems. The various mathematical structures arising during finite element implementation play an important role in solving engineering problems. The talk introduces some of these points.)

 

Lecture 165 (January 24, 2008) Spectral Pick interpolation from a complex-geometric viewpoint

by Dr. Gautam Bharali, Department of Mathematics, IISc, Bangalore.

(Abstract: 

The spectral Pick-interpolation problem is the problem of determining whether there exists a holomorphic map from the unit disc to the class of complex matrices of 
spectral radius less than one that interpolates prescribed data. It has a complicated solution using operator-theory and control-theory methods. The difficulty in
 implementing this solution motivated a new approach pioneered by Agler and Young. Their methods led to a checkable necessary condition for Pick interpolation. But, 
from a complex-geometric viewpoint, it was unclear why the latter condition should be sufficient. In this talk, we will demonstrate that this condition is NOT sufficient. 
We will also present an inequality -- largely linear-algebraic in flavour -- that provides a necessary condition for matricial data for which the Agler-Young-type test 
provides no conclusions.)

 

 

Talks held last year

 

Lecture 164 (November 15, 2007) A commutativity study for certain rings

By Prof. Moharram M. Khan, Centre for Interdisciplinary Research in Basic Sciences (CIRBSc), Jamia Millia Islamia New Delhi.

(Abstract: In the talk, we discuss with the polynomial identities of the form x^s[x,y]x^t-y^p[x^n,y^m]^{r} y^q = 0 and x^s[x,y]x^t + y^p[x^n,y^m]^{r} y^q = 0,  where $s\ge 0, t\ge 0, n\ge 0, p\ge 0, q\ge 0, r > 0, m > 1$ are fixed integers, and also they are different in the noncommutative situation.We first show that: A semiprime ring is commutative if and only if it satisfies the above conditions secondly,commutativity of rings with unity 1 has also been obtained if it  satisfies the defined and some related polynomial identities.Further, the result  for rings with unity 1 is extended to one-sided $s$-unital rings.  Applications and examples are discussed.)

 

Lecture 163 (November 12, 2007) Estimation and Control with Relative Measurements: Scaling Laws and Algorithms.

By Dr. Prabir Barooah, Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA.

(Abstract: Networks of sensors and actuators offer tremendous benefits in diverse areas such as environmental monitoring, healthcare, energy efficient building systems, surveillance, and transportation. For example, a network of ocean and weather condition sensors deployed in a coastal region can provide early warning of storms and tidal surges. Similarly, a  group of small satellites controlled to move in a tight formation can provide high resolution data at a lower cost than a single large satellite. However, to exploit the opportunities of sensor and actuator networks, a number of estimation and control problems have to be tackled. Estimation in large and spatially distributed sensor networks is challenging, and  is exacerbated by the lack of understanding of the minimum estimation error achievable.

 

In the first part of the talk we consider the problem of estimating variables from noisy relative measurements, that is, measurements of the difference between pairs

of variables. This type of measurement model appears in several network problems such as location estimation, time synchronization, and collaborative motion coordination. The problem is naturally posed in terms of a "measurement graph". We examine how the accuracy of the optimal estimate varies with the size of the graph,  obtain scaling laws for the estimation error, and show how the graph structure determines error growth. We then describe distributed algorithms to compute the optimal estimates. The effect of directionality of the graph on the convergence of these algorithms is also discussed.

 

The second part of the talk will briefly introduce a cooperative control problem involving multiple agents, which is again naturally posed in terms of a graph. It turns out that graph structure plays a key role in determining the tracking error due to noisy measurements. This relationship is used to explain certain flocking behavior seen in nature.)

 

Lecture 162 (November 8, 2007, 4:30 PM) Bayesian Inference for Zero-inflated Count Data

By Dr. Archan Bhattacharya, Kolkata.

(Abstract: A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate distribution at zero, with a mixing probability p for the degenerate distribution. This distribution is useful for modeling count data that may have extra zeros. One question is whether the mixture model can be reduced to the power series portion, corresponding to p = 0, or whether there are so many zeros in the data that zero inflation relative to the pure power series distribution must be included in the model i.e., p_0. The problem is difficult partially because p = 0 is a boundary point. Here, we present a Bayesian test for this problem. We compare our Bayesian solution to two standard frequentist-testing procedures.)

 

Lecture 161 (November 5, 2007, 3:30-4:30PM) From Classical Arithmetic to Information Science: Some Applications of Abstract Research

By Prof. Michel Waldschmidt, Institut de Mathématiques de Jussieu, France.

(Abstract: Theoretical research in number theory has a long tradition, in particular in India and in France. Since many centuries, the main goal of these investigations is a better understanding of the abstract theory. Numbers are basic not only for mathematics, but more generally for all sciences; a deeper knowledge of their properties is fundamental for further progress. Remarkable achievements have been obtained, especially recently, as many conjectures have been settled. Yet, a

number of old questions still remains open.

 

Among the unexpected features of recent developments in technology are the connections between classical arithmetic on the one hand, and new methods for reaching a better security of data transmission on the other. We will illustrate this aspect of the subject by showing how modern cryptography is related to our knowledge of some properties of natural numbers. As an example, we explain how prime numbers play a key role in the process which enables you to withdraw safely your money from your bank account using an ATM with your PIN (Personal Identification Number) secret code.)

 

Lecture 160 (November 5, 2007, 2:30-3:30PM) Lecture on Error Correcting Codes: Some Recent Results in Mathematics Related to Data Transmission.

By Prof. Michel Waldschmidt, Institut de Mathématiques de Jussieu, France.

(Abstract: Starting with card tricks, we show how mathematical tools are used to detect and to correct errors occurring in the transmission of data. These so-called "error-detecting codes" and "error-correcting codes" enable identification and correction of the errors caused by noise or other impairments during transmission from the transmitter to the receiver. They are used in compact disks to correct errors caused by scratches, in satellite broadcasting, in digital money transfers, in telephone connections, they are useful for improving the reliability of data storage media as well as to correct errors cause when a hard drive fails. The National Aeronautics and Space Administration (NASA) have used many different error-correcting codes for deep-space telecommunications and orbital missions.

 

Most of the theory arises from earlier developments of mathematics, which were far removed from any concrete application. One of the main tools is the theory of finite fields, which was invented by Galois in the XIXth century, for solving polynomial equations by means of radicals. The first error-correcting code happened to occur in a sport newspaper in Finland in 1930. Claude Shannon created the mathematical theory of information half a century ago. The mathematics behind these technical devices is being developed in a number of scientific centers all around the world, including in India and in France.)

 

 

Lecture 159 (November 1, 2007) Kida's formula in Iwasawa theory

By Dr. Amala Bhave, School of Mathematics, TIFR, Mumbai.

(Abstract: Let E be an elliptic curve defined over a field F. We study the Selmer group of E over an infinte Galois extension L of F as a module over the Iwasawa algebra of the Galois group of L over F. We explain the above terminology in the talk. Towards the end, we state Kida's formula. We try to make it accessible to the students.)

 

Lectures 158 (October 29, 2007) Cooling of Fans in Turbines of Jet Engines

By Prof. R.M. Mattheij, Chair of Scientific Computing, Centre for Analysis, Scientific Computing and Applications (CASA), Technical University, Eindhoven, The Netherlands.

(Abstract: Jet engines have a number of rotators. In particular at the hot end the material may wear due to the interaction with the hot gasses. Basically there are three ways of preventing (or rather slowing down this process)., surface coating, internal cooling and film cooling. In this talk we show how the cooling holes are being made (by electro-chemistry or laser drilling) and how the shape of the cooling holes is impacting this cooling. Numerical modelling and high performance computing are essential in this.)

 

Lectures 156 and 157 (October 11 and October 25, 2007)

By Dr. Ritumoni Sarma, Department of Mathematics, Indian Institute of Technology Guwahati.

(Abstract:: The abstract theory of "Lie algebras" is seemingly analogous to the theory of "rings".  We will start from the definition of a Lie algebra. After introducing the basic definitions and fixing notation we will discuss some important results on finite dimensional  nilpotent and solvable Lie algebras. Also we will see representations of sl(2,F) (traceless 2 × 2-matrices with coefficients from a field F). Finally, we will discuss Cartan-decomposition of a semi-simple Lie algebra.

We will try to make these talks accessible to the one who has gone through a course on algebras (groups or/and rings). We don't assume any earlier

exposure to "Lie algebras".)

 

 

Lectures 155 (September 13, 2007) Structured Perturbation Analysis of Eigenvalue Problems

By Dr. Shreemayee Bora, Department of Mathematics, Indian Institute of Technology Guwahati

(Abstract: Eigenvalue problems arising from various applications often involve matrices that have structures like Hermitian, Skew-Hermitian, symmetry, skew-symmetry or symplectic to name a few. This often  results in symmetries in the distribution of the eigenvalues and it has been observed that algorithms for computing such eigenvalues need to preserve the structure of the problem in order to preserve symmetry in the computed solutions and thus get physically relevant answers. This naturally gives rise to an analysis of the effect of perturbing structured eigenvalue problems in a way that preserves their structures.
 
This talk aims to highlight some very interesting and new results in this fast developing area of research that has received a lot of attention in recent times.)

 

Lectures 153 and 154 (August 30 and September 6, 2007) Ergodic Theory (On flows)

By Dr. Shrihari Sridharan, Department of Mathematics, Indian Institute of Technology Guwahati

(Abstract: In this two-part expository lecture, we shall study the independent ergodic theorem due to Birkhoff and mixing properties of various maps. In the first lecture, we shall revise some elementary mappings and their indecomposable properties. In the second lecture, we shall apply these ideas to geodesic flows on manifolds and some more associated flows. The lectures will be delivered in a fashion to appreciate the historic developments of the subject.)

 

Lecture 152  (May 16, 2007)  Parallel Computational Techniques for Solving Singular Perturbation Boundary Value Problems
By Dr. Rajesh K. Bawa, Department of Computer Science, Punjabi University, Patiala.

 

Lecture 151  (March 29, 2007)  Stokesian Dynamics Simulation for Two Phase Flow

By Dr. Anugrah Singh, Department of Chemical Engineering, IIT Guwahati

(Abstract:
The study of bounded and unbounded flows in the Stokes-flow regime (also
known as microhydrodynamics) finds general application in diverse areas
such as biological fluid mechanics, suspension rheology, colloids,
aerosols and polymers.  The development of numerical technique for such
problems encounters difficulty due to the nature of many body hydrodynamic
interactions, long-range nature of hydrodynamic forces and singularity at
particle contacts. In this talk we present an overview of a recent
numerical simulation technique commonly known as Stokesian Dynamics which
overcomes many of these difficulties and is more efficient for suspension
flow problems. The method of  Stokesian Dynamics in principle is similar
to molecular dynamics simulation of simple fluids except that the forces
driving the particle motion are more complex.  Modification of Stokesian
Dynamics Simulation for bounded flows will be discussed  by considering an
example of plane shear flow between two parallel walls.)

 

 

Lecture 150  (March 22, 2007) Billiards in Rational-Angled Polygons
By Dr. Jayadev Siddhanta Athreya, Department of Mathematics, Yale University, USA.

 

 

Lecture 149  (March 15, 2007) Newton-Rapshson-Simpson Method

By Dr. Durga Charan Dalal, Department of Mathematics, IIT Guwahati

 

 

Lecture 148  (March 9, 2007) Wiener-Hopf Methods in Water Wave Scattering Problems

By Professor Aloknath Chakrabarti, UGC Emeritus Fellow, Department of Mathematics, Indian Institute of Science, Bangalore.

 

Lecture 147  (February 22, 2007) Holonomy Decomposition

By Dr. K.V. Krishna, Department of Mathematics, IIT Guwahati.

 

(Abstract: Krohn-Rhodes decomposition theorem is a celebrated and

fundamental theorem of automata which is a primary decomposition theorem.

Eilenberg's holonomy decomposition theorem for transformation semigroups

is a sophisticated version of Krohn-Rhodes decomposition. In this talk,

after briefing these theorems, the speaker presents the holonomy

decomposition for a class of near-semirings. This work is motivated by the

role of near-semirings in automata.)

 

Lecture 146  (February 15, 2007) Multigrid Methods and Parallel Computations

By Professor Murli M Gupta, Department of Mathematics, The George Washington University, Washington D.C., USA.

 

Lecture 145 (February 12, 2007, 1200 noon, Gallery I) Two Decades of HOC (Higher Order Compact) Schemes for Partial Differential Equations of Mathematical Physics

By Professor Murli M Gupta, Department of Mathematics, The George Washington University, Washington D.C., USA.

 

Lecture 144  (February 8, 2007) Water Wave Scattering by a Sea-bed with Small Undulations

By Dr. Swaroop Nandan Bora, Department of Mathematics, IIT Guwahati.