DEPARTMENT OF MATHEMATICS

INDIAN INSTITUTE OF TECHNOLOGY MADRAS

 

 

                                             

 

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M. Sc.

M. Tech.

Ph. D.

Minor Stream

B. Tech

 

Ph.D. Programme

 

Admission for July-November 2017

Approved candidates list for July-November 2017 admission

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M.Sc.–Ph.D. dual degree in Mathematics

M.Tech.–Ph.D. dual degree in Mathematics

Department conducts various research activities both fundamental and applied. The department offers guidance in the following broad fields of research in Mathematics leading to Doctor of Philosophy degree of the IIT Madras.

 

 

ALGEBRA AND GEOMETRY

Commutative Algebra

Algebraic Combinatorics

Geometry and Topology of Toric Varieties

Group Theory

Algebraic Geometry

 

Linear Algebra

Fuzzy Algebra

Applications of Algebra

Number Theory

 

 

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, a Zumaya algebras and their degenerations, theory of moduli and bi-algebraic structures are being studied.

 

ANALYSIS

Functional Analysis

Numerical Analysis

Complex Analysis

Special Functions

Operator Equations

Inverse and Ill-posed Problems

Harmonic Analysis

Wavelets

Mathematical Programming

Game Theory

Signal / Image Processing

 

Conformal Geometry

Fixed Point Theory and Applications

Fuzzy Set Theory and Analysis

Functional Equations

Spectral Approximation

Non-smooth Analysis

Optimization Theory

Sampling Theory

Approximation Theory

Control Theory

Theory of Fractals

 

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, quasi conformal mappings, generalized Newton methods and applications, optimal best proximity pair solutions, non-smooth optimization, fuzzy set theory and applications, fractals, fractal interpolation, Signal / Image compression based on fractals, CAGD, semi-definite linear complementary problems. Wavelets and their applications.

 

DIFFERENTIAL EQUATIONS AND
APPLIED MATHEMATICS

 

Convective Heat and Mass Transfer

Computational Fluid Dynamics

Ship Hydrodynamics

Non-linear Differential Equations

 

 

Numerical PDE

Sobolev Spaces and PDE

Mathematical Modeling

Fluid Mechanics

Bio-Fluid Mechanics

Integral and Differential Equations

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. Topics of specific interest include higher order semi-compact schemes for viscous incompressible flows, instabilities in thin film systems, regularization techniques for PDEs, 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

 

Applied Probability

Stochastic Processes

Operations Research

 

 

Stochastic Models

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.

 

DISCRETE MATHEMATICS AND
THEORETICAL COMPUTER SCIENCE

 

Theoretical Computer Science

Graph Theory

Combinatorics

DNA Computing

Theory of Codes

Combinatorial Optimization

 

 

Discrete Mathematics

Formal Language

Automata Theory

Modular Computing

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.

 

 

During the programme the research scholars interact with the faculty and students of the department and also with sister departments, and take courses necessary for their research. The weekly seminars/colloquium of the department help them to come in contact with eminent visiting mathematicians and scientists from India and abroad. The duration of programme is 2-5 years.


Placement

After completion of the programme, the scholars get excellent opportunities to join educational and research institutions in India and abroad. The placement office helps the scholars to get jobs in industries. During the last few years, several of our students have joined software industries through campus interviews.