Program Overview

Research Areas under the program

Stochastic Modelling and Analysis,
Semi-group Theory,
Machine Learning and Deep learning,
Graph Theory and Combinatorics,
Inverse problems,
ill-posed problems,
numerical analysis,
Metric fixed point theory,
Genome Rearrangement Problems,
Physics informed Neural Networks

Achievements

100+ Scopus indexed publications
12 Ph.D. scholars
1 Ph.D. awarded

Major Research Areas

Topic Name	Faculty	Description
Graph Theory and Applications	Dr. Manjusha R	The main interest is to study various graph parameter bounds incorporated with other mathematical or fuzzy mathematical tools. A detailed study on the metric dimension of a graph and its applications and analysing different aspects and applications of algebraic graph theory in other fields.
Machine Learning and Deep learning	Dr. Manju B R	N/A
Semi-group Theory	Dr. Muralidharan V	Study of Unit regular monoids
Graph Theory and Combinatorics	Dr. A. V. Prajeesh	The main interest is to deal with certain open problems in the field of graph theory and combinatorics, especially in the field of graph labeling and algebraic graph theory. The interest also comprises of discussions about certain combinatorial objects like magic squares, Kotzig arrays and magic rectangles and there applications in design of experiments.
Metric fixed point theory	Dr. Prajisha E	As there are many generalizations and extensions of the fundamental theorem of metric fixed point theory, known as Banach’s contraction principle, we can concentrate on the coupled version of this theorem and its variants. The main research interest is related to coupled fixed point theorems of different contractive type mappings. In this direction, we have considered different types of metric spaces with and without an ordered structure on it by following the vast literature in this area. As part of future work, we concentrated on coupled fixed points and multivalued fixed points of various contractive and non-expansive type mappings. Simultaneously, analyzing proximal points and different types of iterative techniques for approximation are involved in the theory.
Genome Rearrangement Problems	Dr. Pramod P Nair	Genome rearrangement problems such as reversals, transpositions, and translocations are mathematically formulated as permutations and studied as sorting problems. We study the various types of methods to sort these permutations faster and thus reduce the time complexity of these problems. Genome rearrangements find applications in several areas in bioinformatics and computational biology in analysing DNA, and RNA sequences to study hereditary and rare diseases in humans and animals.
Physics informed Neural Networks	Dr. Pramod P Nair	Physics informed Neural Networks (PINN) which is a recent technique for data-driven solutions of high dimensional PDEs using Deep Neural Networks. PINNs find applications in the faster analysis of complex physical, biological or engineering systems with the same efficiencies as other numerical techniques in the related areas. We look forward to analysing various physical problems related to computational fluid dynamics using PINNs.
Inverse problems, ill-posed problems, and numerical analysis	Dr. Sreedeep C D	The research interest is the analysis of solving ill-posed problems in Banach spaces and mathematical methods in applied sciences, particularly, image processing. Also, to study different numerical iterative methods to solve nonlinear equations and their various types of convergences in Banach spaces and to work on several methods and try to improvise its order of convergence.
Stochastic Modelling and Analysis	Dr. Ushakumari P V	The main research interest is stochastic modelling and analysis with special reference to Queues, Queueing inventory systems, Reliability systems, Reliability inventory systems and operations research.