Rakesh Kumar | Mathematics

Dr. R. K. Dhiman

ResearchGate || G000gle Scholar

Assistant Professor, Dept. of Mathematics,

SRM University-AP, Amaravati Guntur District, Andhra Pradesh, 522240, India

Email: rakeshkumar.r@srmap.edu.in, rakesh1729math@gmail.com, +91-7876986007

ORCID: https://orcid.org/0000-0003-3172-4864

Vidwan-ID : 575709, Socups ID : 58733289100

Research (EUREKA)

Current Research work: Develop an AI-driven techniques to solve eigenvalue problems in wave physics (fluids & optics). Design data-to-prediction models that exploit the relationship between Hermitian and skew-Hermitian problems — enabling efficient solutions for complex wave phenomena.
Areas: Analysis, Mathematical Modelling, Waves,Artificial intelligence
Ph.D. Thesis Title: Non-self-adjoint Eigenvalue Problem for Optical Bent Waveguides (IIT Jodhpur, Rajasthan)
Programming: MATLAB, C++, EIGTOOL, Maple, Mathematica, FDTD, COMSOL, CFD, Python
I want to explore one more area --> understanding the mathematics behind muscle mechanics, strength training, and how exercise builds muscle. I have not explored this deeply yet, but I am very interested in learning more. If you would like to discuss or collaborate, feel free to email me.

Research Work

(1) Rakesh Kumar and Kirankumar R. Hiremath, Non-self-adjointness of bent optical waveguide eigenvalue problem, Journal of Mathematical Analysis and Applications, Elsevier, Vol: 512(1), pg. 126024-126034 (2022) PDF
(2) Rakesh Kumar and Kirankumar R. Hiremath, Mathematical analysis of bent optical waveguide eigenvalue problem, Journal of Physics A: Mathematical and Theoretical, 57 (34),2024 PDF
(3) Rakesh Kumar, Kirankumar R. Hiremath, and Sergio Manzetti, A Primer on Eigenvalue Problems of Non-self-adjoint Operators, Analysis and Mathematical Physics, Springer, 14(21) 2024 PDF
(4) S. Kundal, Rakesh Kumar, Arpit A. Khandelwal, and Kirankumar R. Hiremath, Mathematical Modelling of a Ring Resonator Based Refractive Index Sensor for Cancer Detection Applications, Optical and Quantum Electronics (2023) PDF
(5) S. Kundal, Rakesh Kumar, Arpit A. Khandelwal, and Kirankumar R. Hiremath, CMT-based Fast Analytical Model of a Ring Resonator Refractive Index Biosensor, Optica Sensing Congress (2023) PDF
(6) S. Kundal, Rakesh Kumar, Arpit A. Khandelwal, and Kirankumar R. Hiremath, Modeling and Enhancing the Sensing Performance of Silicon Nitride Slotted Ring Resonator based Refractive Index Sensor , Applied Optics, Optica Publishing Group, 2025 PDF
(7) S. Kundal, Rakesh Kumar, Arpit A. Khandelwal, and Kirankumar R. Hiremath, Coupled mode theory-based analytical model of a ring resonator refractive index sensor incorporating bending loss and dispersion , Photonics and Nanostructures-Fundamentals and Applications, 62, 101308, 2024 PDF
(8) Rakesh Kumar, Abhishek Nimmwat, and Kushal Sharma, Unsteady free convection Williamson nano fluid over a heated permeable stretching sheet under the effects of inclined magnetic field and thermal radiation, (Physics of Fluids, 2025, submitted)
(9) S. Kundal, Rakesh Kumar, Arpit A. Khandelwal, and Kirankumar R. Hiremath, CMT based fast model of label-free disk resonator sensor for HSV detection, (2025) (submitted)
(10) Rakesh Kumar, Analysis and Computation of Turning Points in Optical Straight and Bent Waveguides, (Mathematics and Computers in Simulation, Elsevier, 2025)
(11) Manish Kumar, Rakesh Kumar and Kushal Sharma, Extended Inequalities Between Eigenvalues and Diagonal Entries of Hermitian Matrices and Block Hermitian Matrices, (Indian Journal of Pure and Applied Mathematics, 2025, submitted)

Conferences

International Conference on Non-linear Analysis and Computational Techniques (ICNACT-2024), India, 8 - 10 August 2024 (Coming)
- Talk Title: Analysis and computations of turning points in bent optical waveguide model
CIRM International conference on Mathematical aspects of the physics with non-self-adjoint operators Marseille, 3 - 7 June 2024, France. (Coming)
Spectral theory workshop School of Mathematics, University of Bristol, 4 – 6 September 2023, U.K. (Coming)
34th, International Workshop on Operator Theory and its Applications (IWOTA), University of Helsinki, July 31 - August 4, 2023, Finland.
Mini-courses in Mathematical Analysis, Edificio Paolotti, Via Paolotti 2/a, Padova, June 19 - 23, 2023, Italy.
National Symposium on Mathematics and Applications (NSMA), Department of Mathematics, Indian Institute of Technology Madras, India, December 22, 2022.
- Talk Title: Analysis of non-self-adjoint bent waveguide eigenvalue problem
International Conference on Mathematical Analysis and Applications (ICMAA), Department of Mathematics, National Institute of Technology, Tiruchirappalli, India, December 15-17, 2022.
- Talk Title: Analysis of non-self-adjoint bent waveguide eigenvalue problem
BIRS workshop on Mathematical aspects of the physics with non-self-adjoint operators Banff, Canada, 10 - 15 July 2022.
- Talk Title: Mathematical analysis of non-self-adjoint eigenvalue problem for the bent waveguides
Optics and Photonics Centre, IIT Delhi Summer School on Optics and Photonics (Jointly organized with National Academy of Sciences, India (NASI)-Delhi Chapter) June 6-June 24, 2022
- Talk Title: Mathematical aspects of the bent waveguides
Workshop on Perturbation of Spectral Bands and Gaps, 26 -30 July 2021, the Technical University of Dortmund (virtual), Germany
International Workshop on Operator Theory and its Applications (IWOTA, virtual), Monday 16th - Friday 20th August 2021, Lancaster University, U.K
International Conference on Advanced Research in Applied Sciences (virtual), 25 September 2021 Kurukshetra University, Kurukshetra, India (Got best presentation award)
International Conference on Advances in Differential Equations and Numerical Analysis (ADENA) (virtual), October 12-15, 2020, IIT Guwahati, India

Talk Title: Mathematical aspects of Non-self-adjoint bent waveguide problem

Awards

International Travel Grant SERB India for Visit to IWOTA Workshop, Finland, 2023
International Travel Grant SERB India for Visit to BIRS Workshop, Canada, 2022
CSIR National Eligibility Test, June and December 2017
Best Presentation in Conference 2021

Professors working on Non-self-Adjoint Eigenvalue problems:
Prof. Nikhil Srivastava|| Prof. Michael Levitin|| Prof. C. Tretter|| Prof. David Krejcirik|| Prof. Lyonell Boulton|| Prof. Michael Demuth|| Prof. Ian Wood|| Prof. Petr Siegl|| Prof. Yin T Poon|| Prof. Marco Marletta|| Prof. Mark Embree|| Prof. Rupert L. Frank|| Prof. Ari Laptev|| Dr. Jean-Claude Cuenin|| Prof. Boris Mityagin|| Prof. Marina Chugunova|| Prof. Denis S. Grebenkov|| Prof. L N Trefethen|| Prof. Jussi Behrndt|| Prof. E B Davies|| Prof. Bonnet-BenDhia Anne-Sophie|| Prof. Ovidiu Costin || Prof. Albrecht Böttcher|| Prof. Marko Lindner|| Community || Linear Operators and Their Spectra, E. B. Davies.

Imporatant Web-links

Spectral theory workshop and conference click-1, click-2. || Maths-India Google Group's Website
Non-self-adjoint operators open problems click
UK Spectral Theory Network click
Conferences-1|| Conferences-2
Math Jobs || NA-Digest || M
International Association of Mathematical Physics
Research Seminar || Important Booklet
Euler International Mathematical Institute
Challenge of Spectral Theory of Non-self-adjoint Operator

Millennium Problems The Riemann Hypothesis

Blogs Let's Read / NBHM Question Paper / GRE Math/ A Hilbert Space Problem Book / Planet Math / CSIR 1

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Zero Waste Life
I started Zero Wasted Life in June 2022. I am motivated by this video. Zero waste does not mean you will not use plastic; it also means you will not waste food, water, light, paper, and other resources. Everyone should get started.

100 tips to get zero
6 actionable tips for going zero waste on a budget
Alternates for online order packing
How to reduce your waste? Nila Patty
In India Paperman
How am I changing my daily life toward this? Update soon...

Others

Prof. Hillel Furstenberg: Why I went into mathematics. video.
Dr. Diana Davis three minutes dance video on her thesis.
The best can come only from failures, patience, and repetition.
If you have learned the art of #Silence, there is nothing else that needs to be taught to you.

Postdoctral-1, Postdoctral-2, GIMP, Vanny Deom, Scholar Tree, Curious Mind Magazine, All India Council for Technical Education, Timeline of Mathematics

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