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  • 10:01 AM, Friday, 03 Dec 2021

Department of Mathematics

Mathematical Control Theory

The problems of fundamental interest in control theory are that of controllability, observability and optimal control. We investigate these problems by using efficient tools from the theory of Differential equations and Functional Analysis. We deal with both linear and nonlinear problems.

(Faculty: Dr. Raju K George)

Industrial Mathematics and softcomputing

We invoke various tools from physics and mathematics to arrive at a mathematical model of a real life system. We make use of the softcomputing algorithms like artificial neural networks, genetic algorithms, fuzzy logic technique for the simulation of various real life systems.

(Faculty: Dr. Raju K George)

Suspension Rheology

Studying the effects of particle and fluid inertia for prolate spheroids at low Reynolds numbers under the action of a periodic external force field. In future this work can be extended for the oblate spheroids. The possibility of chaos in the dynamics can be examined. The results of this problem may provide insight into the development of fluids whose rheological properties can be controlled with small changes in controllable parameters. Planned to study the effects of particle and fluid inertia for prolate spheroids in a uniform true dependent flow field at low field at low Reynolds numbers under the action of a periodic external force field.

(Faculty: Anil Kumar C.V )

Time Series Analysis

Presently working in the area of analysis and modeling of naturally occurring series from Ionospheric and Magnetospheric data. Investigating the chaotic dynamics of the time series of Total Electron Content (TEC), the geomagnetic horizontal Intensity (H) and the ring current index (Dst). The analysis based on the calculation of the invariant characteristics such as Lyapunov exponent, Correlation dimension, etc. and of the surrogate data test established the existence of a low dimensional deterministic chaotic system in all cases.

(Faculty: Dr. Anil Kumar C. V )

Mathematical Elasticity, Homogenization, Partial Differential Equations

When the thickness of the elastic body is small, lower dimensional theories have been proposed, depending on mechanical and geometrical nature of the body, as approximations of usual three-dimensional theory. But it is not evident which is the model most suited to a particular case in mind. Consequently, before approximating the exact solution of a given lower dimensional model, we should first know whether it is “close enough” to the exact solution of the three-dimensional model it is intended to approximate. Thus one is lead to the question of mathematically justifying lower-dimensional models starting from the three-dimensional model.

(Faculty: Dr. N.Sabu )

Differential Geometry and its Applications

The main areas of research interest include:

Uniformization Theory

Our interest is to study the geometry of subvarieties of complex tori and the geometry of some special holomorphic fibrations over complex tori. Then try to obtain a global picture in the set up of uniformization theory and understand it further by studying the rigidity of their complex structure or metric structure.

Hamiltonian Dynamical Systems

The symmetry based techniques are implemented using integrals of motion which are quantities that are conserved along the flow of that system. This idea can be generalized to many symmetries of the entire phase space of the dynamical system. This is done by associating a map from the phase space to the dual of the Lie algebra of the Lie group which is acting on the phase space encoding the symmetry. This map, whose level sets are preserved by the dynamics of any symmetric system is referred as the Momentum map of the symmetry. Momentum maps are at the centre of many geometrical facts that are useful in variety of fields of both pure and applied Mathematics. Also these maps are very useful in Physics and Engineering applications.
Another topic of interest is the classification of integrable Hamiltonian systems.

Information Geometry

Information geometry is a branch of Mathematics that applies the techniques of differential geometry to the field of probability theory. Family of probability distributions which constitutes a statistical model has a rich geometric structure as a manifold with Riemannian metric and dual connections. Using this geometric interpretation one can obtain a new insight into the framework of statistical inference and can develop new techniques for inference. Information geometry has got application in wide areas like Statistical Inference, Information Sciences, Signal Processing, Machine Learning, Convex Analysis, Physics and Brain Science.

(Faculty : Dr.K.S.S.Moosath)

Stochastic Modeling & Analysis, Queuing Theory, Queuing Network Models

Modeling and analysis of some queue related problems that can be considered as parts of some future communication systems. Analyzing these type of models mathematically will helps to measure the effectiveness of such systems when these would be really implemented in practice. Also, the development of a theoretical framework and methods of design and implementation of next-generation broad band wireless networks for transmission of multimedia information along extended transport routes.

(Faculty: Dr. Deepak T.G)

Numerical Solutions to Fluid Dynamics

Main interest is to develop novel, efficient and accurate numerical techniques for solving complex problems of fluid dynamics. Construction and implementation of fast numerical algorithms and derivation of approximate mathematical models. Recent interests includes in developing efficient and stable numerical discretization for the Navier-Stokes Darcy coupled fluid flow using C++.

(Faculty: Dr. Natarajan E)

Computational Partial Differential Equations, Finite Element Methods, Finite Volume Methods and Discontinuous Galerkin Methods.

Research interest lies in the domain of computational partial differential equations (PDEs). In particular, in development (with emphasis on both theoretical and computational aspects) of numerical techniques such as: Finite volume element methods, finite element methods, discontinuous Galerkin methods which are used for obtaining accurate and robust numerical solution of PDEs occurring in science and engineering with proper initial and boundary conditions. Some of the recent work includes: discontinuous finite volume approximation of coupled flow-transport problems, immiscible displacement problems, Stokes equations, nonlinear hyperbolic conservation laws and optimal control problems.

(Faculty: Dr. Sarvesh Kumar)

Numerical Analysis and Singularly Perturbed Differential Equations

Main research interest is to construct and analyze efficient numerical techniques based on Finite Difference and Finite Element methods for singularly perturbed differential equations, which arises in the modelling of convection dominated flow problems in fluid dynamics.Recent research work focuses on analyzing the post-processing technique to obtain higher-order parameter-uniform convergence for the numerical solution of the singularly perturbed problems.Other interests include multi-scale methods for homogenization problems.

(Faculty: Dr. Kaushik Mukherjee)

Commutative Algebra

The topics in Commutative Algebra, which relates problems in Affine Algebraic Geometry, e.g., Affine forms, Affine fibrations, Epimorphism problems, Cancellation problems, Derivations, Locally Nilpotent Derivations and allied areas. Other interests of study includes topics related to Algebra, Geometry and Topology.

(Faculty: Dr. Prosenjit Das)

Machine Learning & Data Mining

Machine learning and data mining algorithms are widely applying in the areas like character recognition, spam filtering, fraud detection, object recognition, natural language processing, post flight launch vehicle performance analysis, anomaly detection, intrusion detection, document analysis, search engines, medical diagnosis, chemical analysis, robotic control, weather prediction and marketing.

(Faculty: Dr. Sumitra S)

Control and Inverse Problems for Deterministic and Stochastic Partial Differential Equations

Studying various aspects of deterministic and stochastic partial differential equations. In particular, control of distributed parameter systems associated with reaction diffusion problems and heat conduction models with memory. Studies on various parameter estimation problems by the method of Carleman estimates and optimal control framework. Current work focus on the control of fluid mechanics, which is one of the important subjects in applied mathematics with potential utility in several engineering applications. In this aspect focus is given on the rigorous resolution of the feedback synthesis of optimal control problems for stochastic fluid dynamic models forced by Gaussian and Levy type stochastic forces using dynamic programming approach.

(Faculty: Dr. Sakthivel Kumaraswamy)