Ph. D. Mathematics

Amaravati

A PhD program in mathematics is an advanced academic journey focused on deepening students’ understanding of mathematical theory, developing their research skills, and preparing them for careers in academia, industry, or government. Typically lasting around 4-6 years, these programs involve rigorous coursework in advanced mathematics topics such as algebra, analysis, geometry, and topology, along with specialized electives tailored to students’ research interests.

One of the central components of a PhD in mathematics is the dissertation, where students conduct original research under the guidance of a faculty advisor. This research contributes new knowledge to the field and demonstrates the student’s ability to think critically, formulate hypotheses, and solve complex mathematical problems.

Amritapuri

Ph.D. program in Mathematics aims to develop expertise in a specific mathematical area, fostering critical thinking, problem-solving skills, and the ability to contribute new knowledge to the field.  Mathematics encompasses diverse areas, each with its own unique focus and application. Some broad categories are Stochastic Modelling and Analysis, Semi-group Theory, Number Theory, Machine and Deep learning, Graph Theory and Combinatorics, Inverse problems, ill-posed problems, and numerical analysis, Metric Fixed Point Theory, Genome Rearrangement Problems, Physics informed Neural Networks, Wavelet Analysis.

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. In the Semigroups that arise in the context of transformations or mappings, the set is the domain of the transformations. Number theory has applications in various areas of mathematics and beyond, including computer science, cryptography, and physics.

Genome rearrangement problems such as reversals, transpositions, and translocations are mathematically formulated as permutations and studied as sorting problems. Physics informed Neural Networks (PINN) which is a recent technique for data-driven solutions of high dimensional PDEs using Deep Neural Networks and look forward to analysing various physical problems related to computational fluid dynamics using PINNs.

Banach spaces and concepts from functional analysis are essential tools in both formulating and addressing well-posed and ill-posed problems.  The main interest is to study different numerical iterative methods to solve non-linear equations and their various types of convergences in Banach spaces and to work on several methods and try to improvise its order of convergence.

Wavelet analysis is a mathematical technique used for signal processing and analysis and it allows for a more flexible representation by using functions that are localized in both time and frequency.

Coimbatore

The Department has a team of highly qualified faculty members with research interests in recent and advanced fields in Mathematics, Statistics and Computer Science, such as Analysis, Algebra, Differential Equations, Fluid Mechanics, Multivariate Statistics, Regression Analysis, Numerical Analysis, Number Theory, Artificial Intelligence, Machine Learning related, Data analytics etc. The Department has organized several International and National Conferences with paper presentations and invited talks of high quality and has a good number of research papers published in refereed International and National Journals. The Department’s research activities are supported through extramural funds for various government agencies like National Board of Higher Mathematics (NBHM), Department of Science and Technology DST, etc. Besides teaching and research activities, faculty spend quality time with the students in guiding them through their career prospects/job opportunities.

Kochi

This course offers a comprehensive and rigorous study in advanced mathematical theories and their applications. With a focus on both theoretical foundations and practical research, scholars engage in cutting-edge exploration across various domains such as algebra, analysis, geometry and applied mathematics. Under the guidance of esteemed faculty members, candidates delve into specialized areas of interest, contributing to the advancement of mathematical knowledge. The program fosters a collaborative and interdisciplinary environment, encouraging scholarly exchange and innovation. Graduates emerge equipped with the analytical prowess and research acumen to excel in academia, industry, and beyond, making significant contributions to the field of mathematics.