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Dr Dinesh Kumar
- Assistant Professor
- Area: Mathematics and Basic Sciences
Dr Dinesh Kumar is an Assistant Professor in the area of Mathematics and Basic Sciences at NIIT University (NU). He obtained his PhD from the Department of Mathematics, IIT Guwahati in the area of Mathematical Biology. His current research interests are in Mathematical Biology, Complex Networks, and Graph Partitioning. He has over eight years of experience in research and teaching after his PhD. He has published his research works in reputed international journals.
His current interdisciplinary research work explores a new research avenue within the area of dynamics on complex networks, namely, partitioning of networked dynamical systems that are aware of some dynamical properties of the dynamics in the resulting daughter sub-networks. His work intersects with dynamical systems, spectral graph theory, computer science (particularly graph partitioning) and ecological science (spatial population dynamics).
There are numerous applications of his current work including power system networks and gene regulatory networks. He has applied his work in the ecological context which has resulted two publications of international repute:
- D. Kumar, J. Gupta and S. Raha, “Partitioning a reaction-diffusion ecological network for dynamic stability,” Proceedings of the Royal Society A, 475:20180524, 2019.
- D. Kumar, A. Abhishek, S. Raha, “Stability aware spatial cut of metapopulations ecological networks,” Ecological Complexity, 47, 100948, 2021.
Qualifications
- PhD, Mathematics
- MSc, Mathematics
- BSc Maths, Chemistry, and Computer Application
Experience
- Research – 5.5 Years
- Teaching – 4+ Years
Courses taught
- Function of Complex Variables and Linear Algebra (UG)
- Calculus and Differential Equations (UG)
- Differential Equations and Integral Transforms (UG)
- Complex Analysis, Series Solution and Calculus of Variation (UG)
- Probability & Statistics (UG)
- Topology & Measure Theory (PG)
- Functional Analysis (PG)
- Introduction to Linear and Non-linear Optimization
- Optimization for Data Science
- Numerical methods for Data Science
- Business Statistics
- Remedial Mathematics- I & II
- Linear Algebra and Differential Equations
Research areas
- Applied Mathematics (Mathematical Modelling, Dynamical Systems & Bifurcation Theory, Spectral Graph Theory, Optimal Control Theory, and Computational Mathematics)
- Mathematical Biology
- Complex Networks
- Graph Partitioning
Consulting areas
- Mathematics and its applications
Selected publications
- D. Kumar, A. Abhishek, S. Raha, “Stability aware spatial cut of metapopulations ecological networks,” Ecological Complexity, ISSN:1476-945X, 47:100948, 2021. (IF:1.882)
- D. Kumar, J. Gupta, S. Raha, “Partitioning a reaction-diffusion ecological network for dynamic stability,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN: 1364-5021, 475:20180524, 2019. (IF:2.741)
- D. Kumar, S.P. Chakrabarty, “A predator-prey model with additional food supply to predators: Dynamics and application,” Computational and Applied Mathematics, ISSN: 0101-8205, 37, pp.763-784, 2018. (IF:2.239)
- D. Kumar, S.P. Chakrabarty, “Additional food induced Turing patterns for a diffusive predator-prey model,” International Journal of Applied and Computational Mathematics, ISSN: 2349-5103, 3, pp. 165-183, 2017. (Cite Score: 2.4)
- D. Kumar, S.P. Chakrabarty, “A comparative study of bioeconomic ratio-dependent predator-prey model with and without additional food to predators,” Nonlinear Dynamics, ISSN: 0924-090X, 80(1-2), pp. 23-38, 2015. (IF:5.022)
- R. Kon, D. Kumar, Stability of Rosenzweig-MacArthur models with non-diffusive dispersal on non-regular networks, Theoretical Population Biology, ISSN:0040-5809, 150: 14-22, 2023. (IF:1.514)
Publications
View MoreResearch papers
- D. Kumar, A. Abhishek, S. Raha, “Stability aware spatial cut of metapopulations ecological networks,” Ecological Complexity, ISSN:1476-945X, 47:100948, 2021. (IF:1.882)
- D. Kumar, J. Gupta, S. Raha, “Partitioning a reaction-diffusion ecological network for dynamic stability,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN: 1364-5021, 475:20180524, 2019. (IF:2.741)
- D. Kumar, S.P. Chakrabarty, “A predator-prey model with additional food supply to predators: Dynamics and application,” Computational and Applied Mathematics, ISSN: 0101-8205, 37, pp.763-784, 2018. (IF:2.239)
- D. Kumar, S.P. Chakrabarty, “Additional food induced Turing patterns for a diffusive predator-prey model,” International Journal of Applied and Computational Mathematics, ISSN: 2349-5103, 3, pp. 165-183, 2017. (Cite Score: 2.4)
- D. Kumar, S.P. Chakrabarty, “A comparative study of bioeconomic ratio-dependent predator-prey model with and without additional food to predators,” Nonlinear Dynamics, ISSN: 0924-090X, 80(1-2), pp. 23-38, 2015. (IF:5.022)
- D. Kumar, S.P. Chakrabarty, “Optimal control of pest by supply of additional food to predators in a predator-prey system,” Journal of Advanced Research in Dynamical and Control System, ISSN: 1943-023X, 7(1), pp. 56-65, 2015. (Cite Score:0.41)
Awards and recognition
- Awarded the Junior Research Fellowship by Department of Higher Education, Ministry of Human Resources Development, Government of India, 2009-2011
- Awarded the Senior Research Fellowship by Department of Higher Education, Ministry of Human Resources Development, Government of India, 2011-2014.
- Awarded the NBHM Postdoctoral Fellowship by National Board for Higher Mathematics, Department of Atomic Energy, Government of India, 2017-2018.
- Awarded the Dr D.S. Kothari Postdoctoral Fellowship by University Grants Commission, Government of India, 2018-2021
- Awarded the The Chebyshev Grant by the Russian Mathematical Community to attend ICM 2022 in St Petersburg (event canceled), 2022.
Professional activities and achievements
- Invited talks and seminars:
- ‘Stability Invariant Partitioning of Reaction-Diffusion Metapopulations Networks,’ IIT Palakkad, India, Nov.29, 2021
- ‘Stability Aware Cut of Metapopulations Complex Networks,’ Muthayammal College of Arts & Science, Rasipuram (Tamil Nadu), India, Aug.24, 2021.
- ‘Stabilized Partitioning of Reaction-Diffusion Metapopulations Complex Networks,’ IIT Roorkee, India, Dec.26, 2020.
- ‘Additional Food and Predator-Prey Dynamics,’ 6th China India Japan Korea Mathematical Biology Colloquium Cum Conference, IIT Kanpur, India, Aug.23-26, 2017.
- ‘On Periodic Orbits, Research Scholar Seminar Series,’ Department of Mathematics, IIT Guwahati, Oct. 30, 2012.
- ‘Local Bifurcations of Continuous Dynamical Systems,’ Research Scholar Seminar Series, Department of Mathematics, IIT Guwahati, May 31, 2011.
- Workshops and conferences attended:
- Advanced workshop on ‘Mathematical Theory of Control and Numerics,’ Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, India, Nov.21-30, 2012.
- Workshop on ‘Stability & Bifurcation Analysis and Pattern Formation in Mathematical Ecology and Epidemiology,’ Indian Institute of Technology (IIT), Kanpur, India, Feb.25- Mar.02, 2011.
- Workshop and symposium on ‘Mathematical Ecology,’ Indian Institute of Science Education and Research (IISER), Kolkata, India, Dec.7-14, 2010.
- International workshop on ‘Recent Advances in Computational Fluid Dynamics,’ Indian Institute of Technology (IIT), Guwahati, India, Aug.30- Sep.02, 2010.
- Rajasthan Ganita Parishad- 20th Annual Conference on ‘Emerging Fields in Mathematics and their Interdisciplinary Uses,’ Government College Kota, Rajasthan, India, Jan.18-19, 2009.
- Fellowships received:
- Junior Research Fellowship, awarded by Department of Higher Education, Ministry of Human Resources Development, Government of India, 2009-2011.
- Senior Research Fellowship, awarded by Department of Higher Education, Ministry of Human Resources Development, Government of India, 2011-2014.
- NBHM Postdoctoral Fellowship, awarded by National Board for Higher Mathematics, Department of Atomic Energy, Government of India, 2017-2018.
- Dr D.S. Kothari Postdoctoral Fellowship, awarded by University Grants Commission, Government of India, 2018-2021.
- Qualified ‘National Eligibility Test’ (NET), conducted jointly by Council of Scientific & Industrial Research and University Grant Commission, Government of India, 2008 & 2009
- Qualified ‘Graduate Aptitude Test in Engineering’ (GATE), conducted jointly by Indian Institute of Science & seven Indian Institute of Technology on behalf of Department of Higher Education, Ministry of Human Resources Development, Government of India, 2009
- Professional Memberships
- Indian Mathematical Society (IMS)
- Society for Industrial and Applied Mathematics (SIAM)
- Society for Mathematical Biology (SMB)
Other interests
- Reading and spirituality