Mr. Pranav Kumar| Inverse Problems |PhD Research Scholar at Indian Institute of Science Education and Research Bhopal , India
Pranav Kumar is a Ph.D. candidate in Mathematics at the Indian Institute of Science Education and Research (IISER) Bhopal, India, with expected completion in July 2025. He holds a Master’s degree in Mathematics from IISER Bhopal, where he worked on inverse problems for linear elliptic equations. His research focuses on mathematical problems related to partial differential equations, particularly in the area of inverse problems. Pranav has published several papers in reputable journals, including works on inverse boundary value problems and biharmonic functions. He has presented at multiple international conferences and has received several travel grants, including one to present his work at the 11th International Conference on Inverse Problems in Malta in 2024. He is actively involved in teaching and has served as a teaching assistant in various mathematics courses at IISER Bhopal.
Professional Profile
Orcid
Education
Pranav Kumar began his academic journey with a B.Sc. in Mathematics from Patna Science College in 2019. He then pursued his Master’s degree in Mathematics at IISER Bhopal, where he focused on inverse problems for linear elliptic equations and completed his thesis under the supervision of Dr. Sombuddha Bhattacharyya. Currently, he is a Ph.D. candidate at IISER Bhopal, expected to graduate in July 2025. His doctoral research, also guided by Dr. Bhattacharyya, delves into inverse problems, particularly for higher-order partial differential equations. Pranav’s education has provided him with a strong theoretical foundation and practical expertise in mathematical modeling, making him a rising expert in the field of inverse problems and partial differential equations.
Experience
Pranav Kumar has gained considerable teaching experience as a Teaching Assistant at IISER Bhopal, assisting with courses such as Multivariable Calculus, Complex Variables, and Real Analysis. His experience spans various undergraduate and graduate-level mathematics courses, where he has guided students in understanding complex mathematical concepts. Additionally, Pranav has participated in multiple workshops, conferences, and summer schools related to inverse problems, medical imaging, and partial differential equations, significantly broadening his academic horizons. He has also been involved in delivering talks at various conferences, including the Math Symposium 2024 at IISER Bhopal and the Inverse Problems Student Meet 2024. His academic visits to institutions like TIFR Bangalore and IIT Gandhinagar further showcase his commitment to collaboration and advancing his research.
Research Interests
Pranav Kumar’s research lies at the intersection of inverse problems, partial differential equations (PDEs), and integral geometry. His work primarily addresses the theoretical aspects of inverse problems, focusing on recovering information about a system from limited or indirect observations. He has made significant contributions to the study of inverse boundary value problems for convection-diffusion equations and polyharmonic operators. His research aims to provide deep insights into the behavior of solutions to PDEs, which have broad applications in medical imaging, geophysics, and signal processing. Pranav is particularly interested in higher-order PDEs and their inverse problems, exploring how partial data can be used to solve complex mathematical models. His work is not only mathematically rigorous but also practically relevant to areas like image reconstruction and environmental modeling.
Awards
Pranav Kumar has received several accolades throughout his academic journey. He qualified the Graduate Aptitude Test in Engineering (GATE) in 2021 and the IIT-JAM Mathematics exam in 2019, both of which are highly competitive national examinations. He currently holds a Senior Research Fellowship at IISER Bhopal, which recognizes his potential as a researcher. Pranav was awarded travel grants for presenting at prominent international conferences, including the 11th International Conference on Inverse Problems Modeling and Simulation (IPMS) in Malta, 2024, where he will deliver a talk on inverse problems. These grants reflect his active participation in the global academic community and the value of his research contributions. His strong academic performance and research recognition underline his emerging leadership in the field of mathematics.
Publications
Inverse boundary value problem for the convection–diffusion equation with local data
Local data inverse problem for the polyharmonic operator with anisotropic perturbations
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