
Ph.D. Programme
Admission for JulyNovember 2018
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►Comprehensive Examination
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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, semigroups and fuzzy algebra. More
specifically, a Zumaya algebras and their degenerations, theory of moduli and bialgebraic structures are being studied.

ANALYSIS

Functional
Analysis
Numerical Analysis
Complex Analysis
Special Functions
Operator Equations
Inverse and
Illposed 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
Nonsmooth
Analysis
Optimization
Theory
Sampling Theory
Approximation
Theory
Control Theory
Theory of Fractals

Current Research Interests
Complex
analysis, functional analysis, harmonic analysis, nonlinear analysis,
nonsmooth 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 illposed problems, quasi conformal mappings, generalized Newton
methods and applications, optimal best proximity pair solutions, nonsmooth optimization, fuzzy set theory and
applications, fractals, fractal interpolation, Signal / Image
compression based on fractals, CAGD, semidefinite linear complementary
problems. Wavelets and their applications.

DIFFERENTIAL EQUATIONS AND APPLIED MATHEMATICS

Convective Heat and Mass Transfer
Computational Fluid Dynamics
Ship Hydrodynamics
Nonlinear Differential Equations

Numerical PDE
Sobolev Spaces and PDE
Mathematical Modeling
Fluid Mechanics
BioFluid Mechanics
Integral and Differential Equations
Water Waves

Current Research
Interests
Members of this group work on the applications of
variational principles, biofluid mechanics, convective heat and mass
transfer, computational fluid dynamics, Modeling and simulation. Topics of specific interest include higher order semicompact 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 25 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.
