Dr. Shailesh Kumar Tiwari Department of Mathematics Indian Institute of Technology Patna

Dr. Shailesh Kumar Tiwari

Assistant Professor

Department of Mathematics

Indian Institute of Technology Patna

Bihta, Patna-801 106, Bihar, India

📄 Updated CV (PDF)
42Research Papers
13Invited / Research Talks
4Ph.D Scholars

About Me

My academic journey began with a Ph.D. at Indian Institute of Technology Delhi, where I developed the foundations of my research in ring theory. It subsequently took me across an ocean to a postdoctoral position at the University of São Paulo in Brazil, an experience that broadened both my mathematical perspective and my collaborations, before I returned to India to continue my work at Indian Institute of Science Education and Research Bhopal. I am now privileged to pursue research and teaching at Indian Institute of Technology Patna. Alongside my research, I am deeply committed to teaching, and I take particular satisfaction in making abstract algebra accessible and engaging — helping students move from unfamiliarity to genuine understanding and, ultimately, to a sense of intellectual ownership of the subject.

Research Interests

  • Associative rings and algebras
  • Differential polynomial identities on prime & semi-prime rings
  • Finite Fields
  • Primitive & normal elements over finite fields

Education & Experience

Ph.D. in Mathematics
Indian Institute of Technology Delhi, India
January 2011 – July 2016
Post-Doctoral Fellow
IISER Bhopal, India
Sept 2018 – Dec 2019
Post-Doctoral Fellow
ICMC, University of São Paulo, Brazil
Sept 2017 – Aug 2018
Visiting Assistant Professor & Adjunct Faculty
Dr. B. R. Ambedkar University Delhi, India

Journal Publications

  1. A. Shukla, S. K. Tiwari, Trace of subset of product of sets and r-primitive elements in finite fields, Finite Fields and Their Applications, 115, 102864 (2026). Link
  2. P. Gupta, S. K. Tiwari, V. De Filippis, Actions of annihilating b-generalized skew derivations on Lie ideals, Ricerche di Matematica (2026).Link
  3. A. Choudhary, J. Sharma, S. K. Tiwari, K. Chatterjee, Rational image of r-primitive k-normal elements with prescribed traces, Computational and Applied Mathematics, 45, 370 (2026). Link
  4. P. Gupta, S. K. Tiwari, L. Singh, Multilinear polynomial identities under the action of generalized skew derivations, Ukrainian Mathematical Journal, 78, 81(2026). Link
  5. A. Shukla, K. Chatterjee, S. K. Tiwari, Primitive pair over finite fields with specified quadratic coefficient, Advances in Mathematics of Communications, 23, 1–16 (2026). Link
  6. K. Chatterjee, S. K. Tiwari, H. Sharma, A special type of primitive normal pair in a finite field of odd characteristic, Asian-European Journal of Mathematics (2026). Link
  7. A. Shukla, S. K. Tiwari, On existence of primitive pairs (ξ + ξ⁻¹, f(ξ)) with arbitrary traces, Communications in Algebra, 53(6), 2456–2468 (2025). Link
  8. K. Chatterjee, S. K. Tiwari, A primitive normal pair with prescribed prenorm, Proceedings Mathematical Sciences, 135(6) (2025). Link
  9. B. Dhara, S. K. Tiwari, P. Gupta, M. Bera, Annihilating co-commutators of b-generalized skew derivations in prime rings, Communications in Algebra, 53(11), 4583–4593 (2025). Link
  10. P. Gupta, S. K. Tiwari, Generalized skew-derivations acting as commuting maps on prime rings, Annali dell' Università di Ferrara, 71, 43 (2025). Link
  11. L. Singh, V. De Filippis, S. K. Tiwari, Identities with b-generalized derivations and generalized skew derivations on prime rings, Asian-European Journal of Mathematics, 18(03), 2450117 (2025). Link
  12. K. Chatterjee, H. Sharma, A. Shukla, S. K. Tiwari, Arithmetic progression in a finite field with prescribed norms, Forum Mathematicum, 37(01), 345–357 (2025). Link
  13. P. Gupta, S. K. Tiwari, Generalized skew derivations acting as Jordan homomorphism, Annali dell' Università di Ferrara, 70, 1635–1654 (2024). Link
  14. S. K. Tiwari, P. Gupta, Identities involving b-generalized skew derivations in prime rings acting as Jordan derivation, Communications in Algebra, 52(11), 4612–4630 (2024). Link
  15. V. De Filippis, P. Gupta, S. K. Tiwari, B. Prajapati, Centralizing identities involving generalized derivations in prime rings, Georgian Mathematical Journal, 31(04), 587–605(2024). Link
  16. P. Gupta, V. De Filippis, S. K. Tiwari, Generalized skew-derivations acting on multilinear polynomial in prime rings, Communications in Algebra, 52(01), 48–78 (2024). Link
  17. P. Gupta, S. K. Tiwari, B. Prajapati, Identities involving generalized derivations act as Jordan homomorphisms, Indian Journal of Pure and Applied Mathematics, 55, 731–748 (2024). Link
  18. V. De Filippis, S. K. Tiwari, Sanjay Kumar Singh, Generalized g-derivations on prime rings, Journal of Algebra and Its Applications, 22(02), 2350037 (2023). Link
  19. B. Prajapati, S. K. Tiwari, C. Gupta, b-generalized derivations act as multipliers on prime rings, Communications in Algebra, 50(8), 3498–3515 (2023). Link
  20. S. K. Tiwari, Product and commuting generalized derivations in prime rings, Rendiconti del Circolo Matematico di Palermo Series 2, 72(02), 1377–1397 (2023). DOI
  21. V. De Filippis, B. Prajapati, S. K. Tiwari, Some generalized identities on prime rings and their application for the solution of annihilating and centralizing problems, Quaestiones Mathematicae, 45(2), 267–305 (2022). Link
  22. S. K. Tiwari, B. Prajapati, Generalized derivations acting on multilinear polynomials as Jordan homomorphisms, Ukrainian Mathematical Journal, 74, 1134–1148 (2022). Link
  23. S. K. Tiwari, Identities with generalized derivations in prime rings, Rendiconti del Circolo Matematico di Palermo Series 2, 71, 207–223 (2022). Link
  24. B. Prajapati, S. K. Tiwari, Some commutativity theorem on Banach algebra, Rendiconti del Circolo Matematico di Palermo Series 2, 70, 1041–1049 (2021). Link
  25. C. Arusha, S. K. Tiwari, A note on generalized derivations as a Jordan homomorphisms, Bulletin of the Korean Mathematical Society, 57(3), 709–737 (2020). PDF
  26. S. K. Tiwari, Sanjay Kumar Singh, A note on generalized derivations with multilinear polynomials in prime rings, Communications in Algebra, 48(04), 1770–1788 (2020). Link
  27. S. K. Tiwari, Identities with generalized derivations and multilinear polynomials, Bulletin of the Iranian Mathematical Society, 46(02), 425–440 (2020). Link
  28. S. K. Tiwari, B. Prajapati, Centralizing b-generalized derivations on multilinear polynomials, FILOMAT, 33(19), 6251–6266 (2019). Link
  29. S. K. Tiwari, B. Prajapati, Generalized derivations acts as a Jordan homomorphism on multilinear polynomials, Communications in Algebra, 47(07), 2777–2797 (2019). Link
  30. M. Ashraf, V. De Filippis, S. A. Pary, S. K. Tiwari, Derivations vanishing on commutator identity involving generalized derivation on multilinear polynomials in prime rings, Communications in Algebra, 47(02), 800–813 (2019). Link
  31. S. K. Tiwari, Generalized derivations with multilinear polynomials in prime rings, Communications in Algebra, 46(12), 5356–5372 (2018). Link
  32. S. K. Tiwari, R. K. Sharma, B. Dhara, Some theorems of commutativity on semiprime rings with mappings, Southeast Asian Bulletin of Mathematics, 42(2), 279–292 (2018).
  33. S. K. Tiwari, R. K. Sharma, On Lie ideals with generalized (α,α)-derivations in prime rings, Rendiconti del Circolo Matematico di Palermo Series 2, 67(3), 493–499 (2018). Link
  34. S. K. Tiwari, R. K. Sharma, B. Dhara, Derivations vanishing on commutators with generalized derivations of order two in prime rings, Communications in Algebra, 45(8), 3542–3554 (2017). Link
  35. S. K. Tiwari, R. K. Sharma, Derivations vanishing identities involving generalized derivations and multilinear polynomial in prime rings, Mediterranean Journal of Mathematics (2017). Link
  36. S. K. Tiwari, R. K. Sharma, B. Dhara, Multiplicative (generalized)-derivations on semiprime rings, Beiträge zur Algebra und Geometrie, 58, 211–225 (2017). Link
  37. B. Dhara, K. G. Pradhan, S. K. Tiwari, Engel type identities with generalized derivations in prime rings, Asian-European Journal of Mathematics, 11(04) (2018). Link
  38. S. K. Tiwari, B. Prajapati, R. K. Sharma, Banach algebra with generalized derivations, Asian-European Journal of Mathematics, 10(04) (2017). Link
  39. V. K. Yadav, S. K. Tiwari, R. K. Sharma, Generalized derivations on Lie ideals in prime rings, Asian-European Journal of Mathematics, 10(02) (2017). Link
  40. B. Dhara, K. G. Pradhan, S. K. Tiwari, Left annihilator of identities involving generalized derivations in prime rings, Iranian Journal of Mathematical Sciences and Informatics, 12(2), 139–151 (2017). Link
  41. R. K. Sharma, B. Dhara, S. K. Tiwari, Left annihilator of commutator identity with generalized derivations and multilinear polynomials in prime rings, Communications in Algebra, 44, 3611–3621 (2016). Link
  42. S. K. Tiwari, R. K. Sharma, B. Dhara, Identities related to generalized derivation on ideal in prime rings, Beiträge zur Algebra und Geometrie, 57, 809–821 (2016). Link

Conference Publications

  1. Contributed paper, International Conference on Semigroups, Algebras and Applications (ICSAA), Cochin University of Science and Technology, India, September 17–19, 2015.
  2. Contributed paper, International Conference on Algebra and its Applications (ICAA), Aligarh Muslim University, India, December 15–17, 2014.

Responsibilities

Institutional

Warden, Aryabhatta Hostel (A, B & D Block), IIT Patna
June 2024 – June 2025
Warden, Kalam Hostel (A & B Wing), IIT Patna
June 2023 – June 2024
Associate Warden, Kalam Hostel (A & B Wing), IIT Patna
August 2021 – May 2023

Departmental

Time Table Coordinator — Department of Mathematics
March 2026 – present
M.Sc. Faculty Advisor (2025 Batch)
June 2025 – June 2027
Ph.D Coordinator — Department of Mathematics
January 2024 – January 2025
Ph.D Coordinator — Department of Mathematics
May 2021 – 5 January 2023
DAPC Secretary — Department of Mathematics
April 2020 – May 2022

Invited & Research Talks

  1. Generalized skew derivations on prime rings, Refresher Course in Mathematics, Patna University, February 02–14, 2026.
  2. Action of three generalized skew derivations on multilinear polynomials in prime rings, RACMAS-2026, Shri Mata Vaishno Devi University, January 21–23, 2026.
  3. b-generalized skew derivations on Lie ideals in prime rings, Advances in Ring Theory and Applications 2025 (ARTA25), Italy (online), December 18–19, 2025.
  4. Generalized g-derivations on prime rings, Associative Rings and Algebras with Additional Structures, Italy (online), July 18–20, 2022.
  5. Centralizing b-generalized derivations on multilinear polynomials, In-House Symposium, IISER Bhopal, India, February 08, 2019.
  6. Generalized derivations on prime and semi-prime rings, IISER Bhopal, India, August 23, 2018.
  7. Derivations on prime and semi-prime rings, University of São Paulo, Brazil, May 23, 2018.
  8. Presented a paper at ICARTA-19, December 17, 2019, Aligarh Muslim University, India.
  9. Presented a paper at Commutative Algebra and Algebraic Geometry (CAAG), July 02–06, 2019, IISER Bhopal, India.
  10. Presented a paper at the III Workshop dos Pós-doutorandos do ICMC-USP, São Carlos, Brazil, November 08, 2017.
  11. Presented a paper at ICSAA, Cochin University, India, September 17–19, 2015.
  12. Attended ICAA, Aligarh Muslim University, India, December 15–17, 2014.
  13. Attended ICAA, Aligarh Muslim University, India, November 11–14, 2016.

Academic Visits

Research stays and academic visits.

Postdoctoral Visit — IISER Bhopal
Department of Mathematics, Indian Institute of Science Education and Research, Bhopal, India
September 2018 – December 2019
Postdoctoral Visit — University of São Paulo
ICMC, Universidade de São Paulo, São Carlos, Brazil
September 2017 – August 2018

Collaborators

Frequent research collaborators and co-authors.

  • Prof. Vincenzo De FilippisUniversity of Messina, Italy
  • Prof. Mohammad AshrafAligarh Muslim University, India
  • Prof. Rajendra Kumar SharmaIIT Delhi, India
  • Dr. Basudeb DharaBelda College, West Bengal, India
  • Dr. Balchand PrajapatiDr. B. R. Ambedkar University Delhi, India
  • Dr. Sanjay Kumar SinghIISER Bhopal, India
  • Dr. Pallavee GuptaVIT Vellore (former Ph.D student, IIT Patna)
  • Dr. C. ArushaSNU Chennai, India
  • Dr. Krishna Gopal PradhanRamnagar College, Purba Medinipur, India
  • Dr. Vishal Kumar YadavIndia

Conferences & Workshops Organized

  1. Linear Codes, Code-Based Functions and Magma Computation, LCCFMC-2026, January 17–18, 2026 (with Prof. Om Prakash).
  2. International Conference on Advances of Differential Equations, Computational and AI-Driven Approaches and Pure Mathematics, ICADCA-25, December 15–16, 2025 (with Dr. P. Das, Dr. R. K. Singh and Dr. P. Sushmitha).
  3. Annual Foundation School, AFS-I, December 01–27, 2025 (with Dr. S. K. Singh, Dr. R. K. Singh and Dr. P. Sushmitha).
  4. Annual Foundation School, AFS-II, May 22 – June 17, 2023 (with Dr. N. K. Tomar and Dr. S. K. Singh).
  5. National Mathematics Day, IIT Patna, December 22, 2021 (with Dr. N. K. Tomar and Dr. A. K. Verma).

Awards & Honours

  1. Postdoctoral Fellowship at IISER Bhopal, India, September 2018 – December 2019.
  2. Postdoctoral Fellowship at ICMC, Universidade de São Paulo, São Carlos, Brazil, September 1, 2017 – August 2018.
  3. CSIR Senior Research Fellowship, IIT Delhi, February 2013 – February 2016.
  4. CSIR Junior Research Fellowship, IIT Delhi, January 2011 – January 2013.
  5. Qualified Junior Research Fellowship (CSIR-JRF) examination, CSIR, New Delhi, India, 2010.
  6. Qualified Graduate Aptitude Test in Engineering (GATE), MHRD, Government of India, 2010.

Ph.D Students

Completed
  • CompletedDr. Pallavee Gupta (DST-Inspire) 2020–2025 Thesis: Differential Polynomial Identities on Prime Rings
    Current Position: Assistant Professor, VIT Vellore
  • CompletedDr. Kaustav Chatterjee (NBHM) 2021–2026 Thesis: Primitive normal polynomials over finite fields with some properties
  • CompletedDr. Aastha Shukla (CSIR-UGC) 2021–2026Thesis: Existence results for primitive pairs, r-primitive and k-normal elements over finite fields
Ongoing
  • OngoingMr. Lovepreet Singh (DST-Inspire) 2023 – presentRoll No. 2321MA12
  • OngoingMs. Nikita Kumari (Institute Fellow) 2026 – presentRoll No. 2621MA04
  • OngoingMr. Sanjeet Pandit (CSIR-UGC JRF) 2026 – presentRoll No. 2621MA09

M.Sc. Project Students

Ongoing
  • OngoingMr. Anand Prakash YadavRoll No. 2512MA16
  • OngoingMr. Mohit SinghRoll No. 2512MA06
Completed
  • CompletedMs. Arya DwivediRoll No. 2412MA08
  • CompletedMr. Sayan GhoshRoll No. 2312MA23
  • CompletedMr. Chappdi Vijaya Chandra ReddyRoll No. 2212MA08
  • CompletedMr. Lovepreet SinghRoll No. 2112MA12
  • CompletedMr. Pravin GaupaleRoll No. 2112MA15
  • CompletedMs. Sumita GunriRoll No. 2112MA29
  • CompletedMs. Anu KumariRoll No. 2012MA05
  • CompletedMr. Narayan BiswasRoll No. 2012MA12
  • CompletedMr. Chandan KumarRoll No. 1912MA04

B.Tech Project Students

Ongoing
  • OngoingMr. Pamula Sai BhargavRoll No. 2301mc24
  • OngoingMs. Gaddipati Sri ThanishkaRoll No. 2301MC28
  • OngoingMr. Rayapudi GnaneshRoll No. 2301MC07
Completed
  • CompletedMr. Dhruv GuptaRoll No. 2101MC17
  • CompletedMr. Arka DuttaRoll No. 2101MC08
  • CompletedMr. Utkarsh Khemraj AnavkarRoll No. 2101MC17
  • CompletedMr. Rituparan Singh PariharRoll No. 2201MC32
  • CompletedMr. Roshan Kumar VermaRoll No. 2201MC34

Teaching

Courses taught at IIT Patna.

  • MA001Preparatory Math I
  • MA002Preparatory Math II
  • MA102Mathematics II
  • MA1101Calculus and Linear Algebra II
  • MA217Algebra
  • MA218Complex Analysis
  • MA2207Complex Analysis
  • MA312Number Theory
  • MA421Linear Algebra
  • MA424Complex Analysis
  • MA427Algebra
  • MA4101Algebra
  • MA529Basic Number Theory
  • MA623Number Theory

Contact

Phone
+91-61152-33074
Office
Block-I, Room No. 415,
Department of Mathematics,
Indian Institute of Technology Patna
Bihta, Patna-801 106, Bihar, India
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