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Overview

Ph. D. in Mathematics is a doctoral program offered by the School Physical Sciences, Amrita Vishwa Vidyapeetham, Amaravati, Amritapuri, Bengaluru, Coimbatore and Kochi  campuses.

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Amrita Vishwa Vidyapeetham has not appointed any Agent or Third-Party Client for securing admission in any programme. Students are hereby requested to contact only the toll-free number on our website for any admission related queries.

– Issued In Public Interest By Directorate Of Admissions And Academic Outreach

About the Program

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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.

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Additionally, PhD students in mathematics often engage in teaching or assistantship duties, gaining valuable experience in communicating mathematical concepts and working collaboratively with peers and professors.

Successful completion of a PhD program in mathematics opens a range of career opportunities, including tenure-track positions at universities, research positions in industry or government agencies, or roles in fields such as finance, data science, and cryptography.

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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.

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Deep learning algorithms can segment and identify specific structures or abnormalities in medical images, aiding in treatment planning and precision medicine. The integration of deep learning and machine learning into the medical field has the potential to enhance diagnostic accuracy, treatment efficacy, and overall patient care.

Graph Theory and Applications deals with the study of various graph parameter bounds incorporated with other mathematical or fuzzy mathematical tools, analysing different aspects and applications of algebraic graph theory in other fields. The main interest comprises of discussions about certain combinatorial objects like magic squares, Kotzig arrays and magic rectangles and applications in design of experiments.

Fixed point theory provides a theoretical foundation for understanding and solving problems involving the stability and existence of solutions under various mathematical transformations. The main research interest is related to coupled fixed point theorems of different contractive type mappings.

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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.

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Bengaluru

Since its establishment in 2002, the Department of Mathematics at ASE, Bengaluru, has grown and evolved, focusing on providing research scholars with a strong mathematical foundation and analytical skills. It offers diverse research area, interdisciplinary collaborations, and experienced research guides. From 2007, the Department started offering Ph.D. programs and courses for Ph.D. scholars. Several scholars have already obtained the Doctor’s degree from the Department. Examination for the fundamental course in Mathematics that must be cleared by all research scholars and is conducted by the department in every six months. Currently, 44 research students are doing Ph.D. under the guidance of faculty members of the department. Moreover, our researchers have published numerous high-quality research articles in various international and national journals. In addition, our scholars published quality journal articles as well as reputed conference articles along with their guides.

The department has an ambitious plan to be the best Mathematics departments and to establish an international reputation as a centre for research in Mathematics.

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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.

 

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The vision and mission of the Department of Mathematics aligns with the overall theme of Amrita Vishwa Vidyapeetham, which is to provide education that is rooted in values and aimed at holistic development. Amrita Vishwa Vidyapeetham believes that education should go beyond academics and focus on the individual’s overall development.

 

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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.

Eligibility

Eligibility

Amaravati
  • M.Sc. in Mathematics
Amritapuri
  • Master’s Degree in Mathematics with at least 55% marks in aggregate.
Bengaluru
  • M.Sc. / M.Phil. Mathematics / M.Tech.
Coimbatore
  • Four-year B.S / B.Sc. in Mathematics / Computer Science / Data Science
  • M.Sc. Mathematics
  • M.Sc. Statistics
  • M S/ MCA / M.Sc. Computer Science / Data Science and related fields.
Kochi
  • Candidates must hold a master’s degree in related discipline from a recognized university or institution.

 

Faculty for Guideship

Amaravati
Dr. Srinivasarao Thota
Dr. Srinivasarao Thota
Associate Professor

Dr. V. M. K. Prasad Goura
Dr. V. M. K. Prasad Goura
Assistant Professor (SG)

Dr. Rashmi Prasad
Dr. Rashmi Prasad
Assistant Professor

Amritapuri
Dr. Rajan Sundaravaradan
Dr. Rajan Sundaravaradan
Assistant Professor

Dr. Sreeja V. K.
Dr. Sreeja V. K.
Professor

Dr. Manju B. R.
Dr. Manju B. R.
Associate Professor

Dr. Pramod P. Nair
Dr. Pramod P. Nair
Assistant Professor

Dr. Manjusha R.
Dr. Manjusha R.
Assistant Professor (Sr. Gr.)

Dr Pavithra Celeste R
Dr Pavithra Celeste R
Assistant Professor

Dr. Sreedeep C. D.
Dr. Sreedeep C. D.
Assistant Professor

Dr. A .V. Prajeesh
Dr. A .V. Prajeesh
Assistant Professor

Dr. S. Pitchai Murugan
Dr. S. Pitchai Murugan
Assistant Professor

Bengaluru
Dr. B. Venkatesh
Dr. B. Venkatesh
Chairperson
Associate Professor

Dr. K. V. Nagaraja
Dr. K. V. Nagaraja
Professor

Dr. K. N. Meera
Dr. K. N. Meera
Associate Professor

Dr. Neetu Srivastava
Dr. Neetu Srivastava
Associate Professor

Dr. V. Kesavulu Naidu
Dr. V. Kesavulu Naidu
Associate Professor

Dr. Sarada Jayan
Dr. Sarada Jayan
Assistant Professor

Dr. K. Murali
Dr. K. Murali
Assistant Professor

Dr. Geetha K. N.
Dr. Geetha K. N.
Assistant Professor

Dr. T. V. Smitha
Dr. T. V. Smitha
Assistant Professor (SG)

Dr. Mullai Venthan Selvam
Dr. Mullai Venthan Selvam
Assistant Professor

Dr. J. U. Viharika
Dr. J. U. Viharika
Assistant Professor

Dr. Naveen Kumar R
Dr. Naveen Kumar R
Assistant Professor

Coimbatore
Dr. Somasundaram K.
Dr. Somasundaram K.
Chairperson
Professor

Dr. Shailendhra K.
Dr. Shailendhra K.
Professor

Dr. Palanisamy T.
Dr. Palanisamy T.
Professor

Dr. Deepa Gopakumar O. S.
Dr. Deepa Gopakumar O. S.
Vice Chairperson
Associate Professor

Dr. Radha Iyer R.
Dr. Radha Iyer R.
Associate Professor

Dr. Vinodkumar A.
Dr. Vinodkumar A.
Associate Professor

Dr. Murali Krishna P.
Dr. Murali Krishna P.
Assistant Professor (SG)

Dr. Puvaneshwari P.
Dr. Puvaneshwari P.
Assistant Professor (SG)

Dr. Gayathri K.
Dr. Gayathri K.
Assistant Professor

Praveen I.
Praveen I.
Assistant Professor (SG)

Dr. Paramanathan P.
Dr. Paramanathan P.
Assistant Professor (Sr. Gr.)

Dr. Kiruthika S.
Dr. Kiruthika S.
Assistant Professor (Sr. Gr.)

Dr. Biswambhar Rakshit
Dr. Biswambhar Rakshit
Assistant Professor (SG)

Dr. J. Geetha
Dr. J. Geetha
Assistant Professor (Sr. Gr.)

Dr. V. Pragadeeswarar
Dr. V. Pragadeeswarar
Assistant Professor (Sl. Gd.)

Dr. A. Ramesh Babu
Dr. A. Ramesh Babu
Assistant Professor (Sr. Gr.)

Dr. K. S. Sreeranjini
Dr. K. S. Sreeranjini
Assistant Professor (Sr. Gr.)

Dr. J. Mahalakshmi
Dr. J. Mahalakshmi
Assistant Professor (Sr. Gr.)

Dr. P. Tamilalagan
Dr. P. Tamilalagan
Assistant Professor

Dr. Prakash P
Dr. Prakash P
Assistant Professor

Dr. S. Santhakumar
Dr. S. Santhakumar
Assistant Professor

Dr. Sumathi I. R.
Dr. Sumathi I. R.
Assistant Professor

Dr. Rajitha C. S.
Dr. Rajitha C. S.
Assistant Professor

Dr. G. Poonguzali
Dr. G. Poonguzali
Assistant Professor

Dr. Lolugu Govindarao
Dr. Lolugu Govindarao
Assistant Professor

Dr. M. Ganesh Kumar
Dr. M. Ganesh Kumar
Assistant Professor

Dr. Sangeeta Kumari
Dr. Sangeeta Kumari
Assistant Professor

Dr. Sekar E
Dr. Sekar E
Assistant Professor

Dr. K.S. Ravichandran
Dr. K.S. Ravichandran
Distinguished Professor

Dr. Devika V.
Dr. Devika V.
Assistant Professor

Dr. Mageshwari V.
Dr. Mageshwari V.
Assistant Professor

Dr. P. Sriramakrishnan
Dr. P. Sriramakrishnan
Assistant Professor

Dr. Kirubavathi G.
Dr. Kirubavathi G.
Assistant Professor

Dr. Neha Singh
Dr. Neha Singh
Assistant Professor

Diya Bhattacharyya
Diya Bhattacharyya
Assistant Professor

Kochi
Dr. Archana Nair
Dr. Archana Nair
Assistant Professor (Sr. Gr.)

Dr. Sreekanth K. M.
Dr. Sreekanth K. M.
Assistant Professor

Dr. T. Senthilkumar
Dr. T. Senthilkumar
Assistant Professor

Research Areas

Amaravati

Computer Algebra 

Numerical Analysis 

Mathematical Modelling  

Computational Finance 

Differential Equation 

Solid mechanics  

Generalized thermoelasticity  

Wave propagation

Variational principle 

Amritapuri

Stochastic Modelling and Analysis 

Number Theory 

Semi-group Theory  

Machine Learning and Deep learning  

Physics informed Neural Networks  

Graph Theory and Applications  

Metric Fixed Point Theory  

Stochastic modelling and distribution theory 

Inverse problems, ill-posed problems, and numerical analysis   

Graph Theory and Combinatorics 

Wavelet analysis 

Bengaluru

Numerical Methods 

Finite Element Method 

Computational Sciences 

Optimization Techniques 

Numerical Mathematical Logics 

Graph Theory 

Fluid Mechanics 

Fluid Dynamics 

Mathematical Modelling 

Computational Mathematics 

Real Analysis 

Coimbatore

Graph Colorings, Graph Indices and Graph Algorithms

Domination, Graph Indices 

Graph Colorings and Graph Indices 

Fem with Wavelets and B-splines 

Hybrid numerical methods for Singularly Perturbed Problems  

Inventory control  

Singularly perturbed PDE 

Numerical Methods on Singularly Perturbed Differential Equations  

Statistical Inference and Six Sigma 

Estimation in Robust Regression 

Designing of control charts 

Statistical inference based on lifetime probability distributions  

Hematocrit depended on viscosity of blood and cardiovascular problems 

 B-splines Methods 

Investigation of pulsatile blood flow behaviour in human large arteries 

Mathematical models for heat transfer system  

Fractional differential equations 

Mathematical Models for semiconductor devices 

Mathematical Modelling of disease transmission 

Fractional nonlinear PDEs, Lie group analysis, Conservation laws, Non-linear PDEs and ODEs 

Generalization of fuzzy numbers and multi-criteria decision models  

Deciphering HIV infection models 

Approximation of Fractal interpolation surfaces 

Functional Analysis 

Time series models, deep neural network models and hybrid models   

Reservoir Computing 

Fractal based image classification 

Multi Criteria Decision Making, Medical Image Processing   

Linear Algebra     

Coding Theory  

Coding Theory and Ring Theory 

Graph based Deep learning models, Data Networks, Medical Image Processing   

Fuzzy DEMATEL and Fuzzy VIKOR in health care    

Pattern Classification and Clustering  

Multi Criteria Decision Making, Medical Image Processing     

Stability analysis and control system of differential equations   

Dynamical Robustness in a network of oscillators.    

Stability analysis of dynamical system  

Prey-predator modelling by considering 
Allee and fear effects  

Number theory 

Highly Composite Numbers    

Kochi

Climate Modelling  

Queueing Theory 

Non-linear Dynamical Systems and control  

Fundings / Projects

Amritapuri
Title of the Project Funding Agency
Stochastic Modelling and Analysis of Connectivity Reliability in 6G IoT Networks using k –out-of- n systems Amrita Vishwa Vidyapeetham (Internal Seed Grant)
Bengaluru

Title of the Project 

Funding Agency 

Finite Element Methods in Haemodynamic Applications 

NBHM 

Coimbatore
Title of the Project Funding Agency
Studies on Qualitative Properties of Single and Multivalued Fractional Stochastic Differential Equations of Higher Order NBHM
On Punctured Codes of Zq-Simplex Codes NBHM
Extensions of Wavelet Packet transform to generalized functions SERB CORE
Total Coloring for Certain Classes of Cayley Graphs DST
Best proximity point iteration for various types of non-self-mappings NBHM
Behzad – Vizing Conjecture on Graph Coloring for Product Graphs DST-SERB
Stability and Stabilization of Random Impulsive Control systems DST-SERB
Total Coloring Conjecture for Certain Classes of Graphs NBHM
“Existence of best proximity points for the sum of two operators” NBHM

Facilities / Research Infrastructure

Amritapuri

Amrita Vishwa Vidyapeetham, Amritapuri

  • High Performance Computing Platform and Research Lab.
Coimbatore

Amrita Vishwa Vidyapeetham, Coimbatore. 

High Performance Computing Platform:  

  • Number of Nodes: 5
    Master Node (1) Configuration: DELL PowerEdge R740 Server with Dual Intel Xeon Gold 5120 2.2G 14 Core Processors; 128GB RAM, 1 x NVIDIA Tesla V100 GPU.   
  • Compute Nodes (4) Configuration: DELL PowerEdge R740 with Dual Intel Xeon Gold 5120 2.2G 14 Core Processors; 256GB RAM, 1 x NVIDIA Tesla V100 GPU.
    Interconnect: Mellanox – InfiniBand; 12 56 Gbps ports.
    Campus Connect: Ethernet 10 Gbps.
    Storage: DELL Power Vault MD3400, 29TB. 

Contact Us

Ph.D. Coordinator (Amaravati)

Dr. Srinivasarao Thota

Associate Professor
Department of Mathematics
Amrita School of Physical Sciences
Amrita Vishwa Vidyapeetham, Amaravati
Andhra Pradesh-522503, India
Email: t_srinivasarao@av.amrita.edu
9182316071

Ph.D. Coordinator (Amritapuri)

Dr. Manjusha R,
Assistant Professor (Senior Grade),

Amrita School of Physical Sciences, Amritapuri
Amrita Vishwa Vidyapeetham, India. 
manjushar@am.amrita.edu 

Ph.D. Coordinator (Bengaluru)

Dr. Mullai Venthan SELVAM 
Assistant Professor
s_mullai11@blr.amrita.edu

Ph.D. Coordinator (Coimbatore)

Dr. A. Vinodkumar
Associate Professor,
Amrita School of Physical Sciences, Coimbatore,
Amrita Vishwa Vidyapeetham, India.
Phone: 0422-2685601
a_vinodkumar@cb.amrita.edu

Ph.D. Coordinator (Kochi)

Dr. T. Senthil Kumar 
Assistant Professor
tsenthilkumar@kh.amrita.edu

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