About
Dr. Arnab Patra is an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Bhilai. His research interests lie in Functional Analysis, Operator Theory, Matrix Analysis, and Spectral Theory. His current work focuses on generalized numerical ranges, Berezin transforms, Toeplitz operators, sectorial operators, operator inequalities. He actively supervises research students and welcomes motivated students interested in operator theory, functional analysis, and related areas. He has over eight years of teaching and research experience.
Research Interests
- Operator Theory
- Functional Analysis
- Matrix Analysis
- Spectral Theory
- Numerical Range Theory
- Berezin Symbol & Berezin Range
- Toeplitz Operators
- Hardy Space Operators
- Semi-Hilbertian Operator Theory
- Operator Inequalities
Academic Background
- Ph.D. in Mathematics
Indian Institute of Technology Kharagpur - M.Sc. in Mathematics
Indian Institute of Technology Kharagpur - B.Sc. in Mathematics
Midnapore College (Autonomous), Vidyasagar University
Professional Experience
- Assistant Professor
Department of Mathematical and Computational Sciences
Indian Institute of Technology Bhilai
April 2021 – Present - Scientist 'B'
Advanced Numerical Research and Analysis Group
Defence Research and Development Organisation (DRDO)
August 2018 – March 2021 - Assistant Professor
Birla Institute of Technology, Mesra
January 2018 – July 2018
Selected Publications
For the complete publication list, please visit my Google Scholar Profile.
- S. Saha and A. Patra. Convolution operators on weighted Hahn spaces. Monatshefte für Mathematik, 2026. DOI
- F. Kittaneh, A. Patra, and J. Rani. On the estimation of the q-numerical radius via Orlicz functions. Journal of Computational and Applied Mathematics, 482, Article 117340, 2026. DOI
- K. Feki, A. Patra, J. Rani and Z. Taki. Joint q-numerical ranges of operators in Hilbert and semi-Hilbert spaces. Linear and Multilinear Algebra, 74(3), 294–316, 2026. DOI
- J. Rani and A. Patra. q-Numerical radii of sectorial matrices and 2×2 operator matrices. Filomat, 39(30), 10609–10630, 2025. DOI
- A. Patra and F. Roy. On the estimation of q-numerical radius of Hilbert space operators. Operators and Matrices, 18(2), 343–359, 2024. DOI
- A. Patra, P. D. Srivastava. Spectrum and fine spectrum of generalized lower triangular triple band matrices over the sequence space ℓp. Linear and Multilinear Algebra, 68(9), 1797–1816, 2020. DOI
Research Guidance
Doctoral Students
- Dr. Jyoti Rani (Awarded: March 2026)
Thesis: A Study of Spectra and Generalized Numerical Ranges of Bounded Linear Operators
Placement Profile: Postdoctoral Researcher at IISER Mohali & Visiting Researcher at Ritsumeikan University, Kyoto, Japan - Sayan Saha (Ongoing)
- Debarati Bhattacharya (Ongoing)
M.Sc. Project/Thesis Supervision
- Nisha Paul (2026)
- Sanju Hazara (2025)
- Biroja Boro (2024)
- Bikash Kisan (2023)
Sponsored Research Project
| Funding Agency | Project Title | Role | Duration | Amount | Status |
|---|---|---|---|---|---|
| SERB (SRG) | Estimation of Numerical Radius and Davis–Wielandt Radius in C*-Algebra | Principal Investigator | 2021–2023 | ₹13.51 Lakhs | Completed |
Teaching Experience
The following undergraduate and postgraduate courses have been taught at IIT Bhilai.
| Course Code | Course Title | Level |
|---|---|---|
| MAL502 | Functional Analysis | PG Core |
| MA605 | Operations Research | UG / PG Core |
| IC152 | Linear Algebra II | UG Core |
| IC153 | Calculus I | UG Core |
| IC202 | Calculus II | UG Core |
| MA500 | Real Analysis | PG Core |
| MA501 | Linear Algebra | PG Core |
| MAL100 | Mathematics I | UG Core |
| MAL010 | Preparatory Course (Mathematics) | UG Core |
| MAL501 | Complex Analysis | PG Core |
| MAL600 | Introduction to Spectral Theory | PG Elective |
Institutional Responsibilities
- Faculty-in-Charge, Student Mentorship Program (SMP), IIT Bhilai, 2022-2023.
- Faculty-in-Charge, Pakdarpanalaya (Mess Block), IIT Bhilai, 2023-2024.
Awards and Honours
- UGC NET JRF in Mathematics, AIR 47.
- GATE in Mathematics, AIR 33.
- INSPIRE Fellowship for Ph.D., Department of Science and Technology, Government of India, (Not availed).
- Joint Admission Test for M.Sc. (JAM), Mathematics, AIR 118.
- INSPIRE Scholarship (SHE), Department of Science and Technology, Government of India, awarded during undergraduate and postgraduate studies.
Invited Talks
- Recent Advances in Applied Mathematics (RAAM 2026)
Mini-Symposium Speaker, Indian Institute of Technology Hyderabad, July 6–8, 2026. - National Conference on Emerging Trends in Mathematical Sciences: Analysis, Modelling, Computation and Algebra (NCETMS-AMCA 2026)
Jadavpur University, March 12–13, 2026. - Young Scientist Symposium
International Conference on Mathematical Sciences and Engineering (ICMSE 2025), Mizoram University, June 9–11, 2025. - Expert Lecture
B.Tech. Mathematics Programme, Krishna Engineering College, Durg, 2025. - Invited Lecture
Workshop on Quantum Computing, University Institute of Information Technology, Himachal Pradesh University, September 2–6, 2019. Topic: Mathematics Required for Quantum Computing