DEPARTMENT OF MATHEMATICS

INDIAN INSTITUTE OF TECHNOLOGY MADRAS

 

 

                                             

 

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Department Profile

ALGEBRA

Ø Commutative Algebra

Ø Algebraic Combinatorics

Ø Geometry and Topology of Toric Varieties

Ø Group Theory

Ø Fuzzy Algebra

Ø Linear Algebra

Ø Algebraic Geometry

Ø Applications of Algebra

Current Research Interests

The focus of research is in the areas of applied algebra, algebraic geometry, commutative algebra, semi-groups and fuzzy algebra. More specifically, azumaya algebras and their degenerations, theory of moduli and bi-algebraic structures are being studied.

ANALYSIS

Ø Functional Analysis

Ø Numerical Analysis

Ø Complex Analysis

Ø Functional Spaces

Ø Special Functions

Ø Operator Equations

Ø Inverse and Ill-posed Problems

Ø Harmonic Analysis

Ø Wavelets

Ø Mathematical Programming

Ø Game Theory

Ø Conformal Geometry

Ø Fixed Point Theory and Applications

Ø Fuzzy Set Theory and Analysis

Ø Functional Equations

Ø Summability Theory

Ø Spectral Approximation

Ø Non-smooth Analysis

Ø Optimization Theory

Ø Sampling Theory

Ø Approximation Theory

Ø Control Theory

Current Research Interests

Complex analysis, functional analysis, harmonic analysis, nonlinear analysis, non-smooth analysis, control theory and optimization theory are the areas studied by the faculty of this group. Topics of research are: approximate solutions of operator equations, inverse and ill-posed problems, generalized inverses and applications, quasi conformal mappings, generalized Newton methods and applications, optimal best proximity pair solutions, iterative functional equations, non-smooth optimization, fuzzy set theory and applications, fractals, fractal interpolation functions, semi-definite linear complementary problems. Wavelets and their applications

APPLIED MATHEMATICS

Ø Numerical PDE

Ø Convective Head and Mass Transfer

Ø Computational Fluid Dynamics

Ø Ship Hydrodynamics

Ø Mathematical Problems related to Naval Architecture and Ocean Engineering

ØMathematical Modeling

Ø Non-linear Differential Equations

Ø Fluid Mechanics

Ø Bio-Fluid Mechanics

Ø Integral and Differential Equations

Ø Water Waves

 

Current Research Interests

Members of this group work on the applications of variational principles, bio-fluid mechanics, convective heat and mass transfer, computational fluid dynamics, modeling and simulation and ship hydrodynamics. Topics of specific interest include anomalies in quantum theory, Lattice Boltzmann method, higher order semi-compact schemes for viscous incompressible flows, instabilities in thin film systems, regularization techniques for PDE’s, applied integral equations and water waves and wave structure interactions. Calculation of the Casimir energy density in flat and curved spaces, trace anomalies with Dirichlet boundary conditions.

APPLIED PROBABILITY AND STOCHASTIC PROCESSES

Ø Applied Probability and Stochastic Processes

Ø Operations Research

Ø Stochastic Models

Ø Mathematical Ecology

Current Research Interests

Research is focused on applied probability and stochastic models, operations research and theory of fuzzy sets, communication network problems, option pricing models, queuing models and stochastic inventory problems.

THEORETICAL COMPUTER SCIENCE AND DISCRETE MATHEMATICS

Ø Theoretical Computer Science

Ø Graph Theory

Ø Combinatorics

Ø DNA Computing

Ø Theory of Codes

Ø Combinatorial Optimization

Ø Discrete Mathematics

Ø Formal Language

Ø Automata Theory

Ø Modular Computing

Ø Approximation Algorithms

 

Current Research Interests

Graph theory, algebraic theory of automata, combinatorial optimization, approximate algorithms and mathematical logic are the areas in which research is undertaken by this group. Knowledge compilation, discrete optimization problems of interconnection networks of multiprocessor systems and unconventional methods of computation are among the topics of special investigation.