Ph.D: 10 Awarded (3 under co-supervision) and 2 Ongoing.

M.Tech. : 17 Completed and 3 Ongoing

1. Engineering Mathematics 2 (MA 102)
2. Algebra (MA 111)
3. Linear Algebra (MA 311)
4. Information and Coding Theory (CSM 322)
5. Theory of Rings and Modules (MA 511)
6. Abstract Algebra (MA 515)

Selected Published Papers

• Ashok Ji Gupta and Sonal Gupta, "Direct Projective Modules and Its Generalizations" Journal of Algebra and its Applications (Accepted May 2025).
•  Satish Kumar, Indivar Gupta and Ashok Ji Gupta, "Quantum Secure Digital Signature Scheme Based on Multivariate Quadratic Quasigroups (MQQ)” Advances in Mathematics of Communications, 2025, 19(5): 1336-1359. doi: 10.3934/amc.2024057 
• Satish Kumar, Harshdeep Singh, Indivar Gupta and Ashok Ji Gupta, "A class of Error-Detecting Codes Based on T-Quasigroups". Journal of Algebra and its Applications, pp18, 2024, DOI: 10.1142/S0219498826500076
• Pradeep Rai, Bhupendra singh and Ashok Ji Gupta, "Quantum and LCD codes from Skew Constacyclic Codes over a General Class of Non-chain Rings" Quantum Information Processing, vol 23, issue 7, pp 58 pages (2024).
• Pradeep Rai, Bhupendra singh and Ashok Ji Gupta,; “ On Quantum and LCD codes from the cyclic codes over the Ring   F q [u, v, w]/[ u 3 -u,  v 2 -v, w 2 -w, uv, vu, uw, wu, uv-vu] ” Journal of Applied Mathematics and Computing, vol 70 issue 2 pp 2141-1262 (2024).  
• Sonal Gupta and Ashok Ji Gupta, “Pure direct projective modules”, Palestine Journal of Mathematics, Vol. 12, No. 3, 408-415, 2023.
• Sonal Gupta and Ashok Ji Gupta, “Finite direct projective modules”, Asian European Journal of Mathematics, Vol 16, No 12, 2350218, 2023, doi:10.1142/S1793557123502182.
• Kaushal Gupta and Ashok Ji Gupta, “Pure C3 Modules”, Asian European Journal of Mathematics, Vol 16, No 12, 2350219, 2023, doi: 10.1142/S1793557123502194.
• Shiv Kumar and A. J. Gupta, “Principally Quasi Dual-Baer Modules”, Palestine Journal of Mathematics, Vol. 12 (Special Issue III), 1–7, 2023.
• Satish Kumar, Harshdeep Singh, Indivar Gupta and Ashok Ji Gupta, "MDS codes based on orthogonality of Quasigroups", Applicable Algebra in Engineering, Communication and Computing, 2023, doi: 10.1007/s00200-023-00631-5.
• Shiv Kumar and A. J. Gupta, “Purely Extending modules and their Generalizations”, Kyungpook Mathematical Journal, vol. 63, 15-27, 2023.
• A. J. Gupta and Sanjeev Kumar Maurya: “On modules whose closed M-cyclic submodules are summand”, Advances in Pure and Applied Algebra (Proceedings of the CONIAPS International Conference 2021), pp 65-70, De Gruyter, 2023, doi: 10.1515/9783110785807-008.
• Satish Kumar, Indivar Gupta and A. J Gupta, “A Study on the Public Key Cryptosystems Based on Quasigroups”, Cryptologia, 1-28, 2022, doi: 10.1080/01611194.2022.2081824.
• Sanjeev Kumar Maurya and A. J. Gupta: “Characterization of rings using finite-direct-injective modules”, Asian European Journal of Mathematics, Vol 13, No 07, 2050133, 2020.
• S. K. Maurya and A. J. Gupta: “Finite Direct Injective modules”, International Electronic Journal of Algebra, Vol. 23, pp 143-152, 2018.
• Manoj Kumar Patel, Varun Kumar and A. J. Gupta: “On Semi-Projective Modules and their Endomorphism Rings”, Asian European Journal of Mathematics, Vol. 11, No.1, 1850029(1-20), 2018.
• A. J. Gupta, B. M. Pandeya, A. K. Chaturvedi: “SP-Injectivity of Modules and Rings”, Asian European Journal of Mathematics, Vol. 5, No: 4, pp.1-7, 2012.
• V. Kumar, A. J. Gupta, B. M. Pandeya, and M. K. Patel: “M-SP-Injective Modules”, Asian European Journal of Mathematics, Vol. 5, No. 1, pp. 1-11, 2012.
• V. Kumar, A. J. Gupta, B. M. Pandeya, and M. K. Patel: “M-C-pseudo injective modules”, East-West J. of Mathematics, Vol-14, No-1, pp. 68-76, 2012.
• B. M. Pandeya, A. K. Chaturvedi,  A. J. Gupta:  “Applications of Epi-Retractable modules”, Bulletin of Iranian Mathematical Society, Vol. 38, No. 2,  pp. 469-477, 2012.
• A. K. Chaturvedi, B. M. Pandeya and A. J. Gupta: “Quasi-pseudo-principally injective modules”,  Algebra Colloquium, 16, no-3, 397-402, 2009.
• A. K. Chaturvedi, B. M. Pandeya and A. J. Gupta: “Quasi c-Principally injective modules and Self-c-Principally Injective Rings”, Southeast Asian Bulletin of Mathematics, 33, 685-702, 2009.

1. Organized a National Instructional Workshop on Cryptology: Code based Cryptography (NIWC-2023) during July 05-07, 2023.
2. A QIP short term workshop on “Algebra, Analysis and Applications” organized jointly as course coordinator with Prof. S K Upadhyay in the Department of Mathematical Sciences, IIT(BHU), Varanasi from 03 July-09 July 2017. 

• Life member, Indian Mathematical Society
• Life member, Cryptology Research Society of India

1. General Mathematics Notes (GMN)
2. Thai Journal of Mathematics
3. Asian European Journal of Mathematics
4. Proceedings of Indian National Science Academy (INSA)
5. Palestine Journal of Mathematics
6. MathSciNet
7. Journal of Algebra and Its Applications

• "Development of Cryptographically efficient lightweight MDS matrices and its extension to code based PQC” (Principal Investigator, R&D/SA/DRDO/Math/22-23/01/367), amount: INR 23.10 Lakhs.

• Convener DPGC of the department from 01 Sep 2022- 07 Sep 2023.
• Member of Departmental Faculty Affairs Committee (DFAC) from January 1, 2023 to continue.
• Chairman, PG Admission Committee of the department (even semester 2018-19,  odd semester 2019-20, even semester 2022-23 & odd semester 2023-24).
• Member of Purchase committee of the department 2018-19.
• Examination-in-Charge of the department 2017-18, 2018-19.
• Convener DUGC of the department from 01 Sep 2015 to 31 Aug 2017.
• Member of Academic Performance Evaluation Committee(APEC) of IIT(BHU) 2017. 
• Member, DPGC department of Mathematical Sciences, IIT(BHU) 2014-15, 2015-16, 2018-19.
• External Member of Board of Studies of VBS Purvanchal University, Jaunpur, 2015-16, 2016-17.
• External Member of Research Degree Committee (RDC) of VBS Purvanchal University, Jaunpur, 2015-16, 2016-17.
• Warden in Limbdi and Vishvakarma Hostel, Admin Warden in Vishveswaraya Hostel IIT(BHU). 
• Members of several co-ordination committees and conveners in the different courses of the Department of Mathematical sciences.
• Member in organizing committee of two conferences of the department in 2011, 2012 and one conference of Indian Mathematical Society, Jan. 2013.
• Member in Time-Table committee of the department in session 2009-10, 2010-11 and 2016-17.

List of Invited Talk/Presented Papers in the Conferences

1. Presented a paper   entitled “Direct projective modules and their Generalizations” in the Fourth International Conference on Mathematics and Statistics,  held at the American  University of Sharjah, Sharjah-UAE, February 20-22, 2025.
2. Gave an Invited talk on “ Purely Essentially Bear Modules" in the XXXVI Ohio State-Denison Mathematical conference, The Ohio State University, Columbus, Ohio-USA (online/offline conference in the memory of Prof. Tariq Rizvi) May 10-12, 2024.
3. Delivered an Invited talk on “Extending module and its generalizations” in the International Conference on "Recent Advances in Pure & Applied Algebra (RAPAA)” held at NIT Jamshedpur, India during October 26-28, 2021.
4. Delivered an Invited talk on “On Finite-Direct-injective modules” in the International Conference on Non Commutative Rings and their Applications, VII (online conference dedicated to Prof. Tariq Rizvi) July 5-7, 2021.
5. Delivered an Invited talk on “A note on Direct-Projective modules” in the the International Conference on Recent Advances in Algebra Analysis and Applications (ICRAAAA-2019), held in the Department of Mathematics and Statistics, Mohanlal Sukhadis University, Udaipur, Rajasthan (India) December 20 - 22, 2019.
6. Delivered an Invited talk on “Finite-Direct-injective modules” in the International Conference on Algebra and Continuum Mechanics, held in the Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, India on November 23-25, 2018. 
7. Delivered an Invited talk on “A Note on Direct-injective modules” in the Conference on Rings and Factorizations, held at University of Graz, Graz, Austria during February 19-23, 2018.
8. Chaired a session in 32^nd Annual national conference of Mathematical Society, Banaras Hindu University On Recent trends in Mathematical Analysis and its Applications held in the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi during February 17-18, 2017.
9. Presented a paper entitled “C-pseudo Injective Modules” in the International Conference on Algebra and its Applications (ICAA-16) held in the Department of Mathematics, Aligarh Muslim University, Aligarh, India during November 12-14, 2016.
10. Presented a paper “M-SP-Injective modules” in the 18^th international conference of International Academy of Physical Sciences on recent trends in Mathematics organized by Faculty of Science, University of Allahabad, Allahabad in collaboration with United Group of institutions, Allahabad during December 22-24, 2015. 
11. Presented a paper “Some properties of pseudo projective modules” in the international conference on recent trends in Mathematics organized by Department of Mathematics, University of Allahabad, Allahabad, during July 10-12, 2015.
12. Delivered an Invited talk on “Endomorphism rings of Pseudo Projective modules” in the seventh China-Japan-Korea international conference on Ring Theory, held at Zhejiang University of Technology, Hangzhou, China during July 1-7, 2015.
13. Delivered an invited talk on “S P Injectivity of Modules and Rings” in the 21^th Annual conference of The Jammu Mathematical Society, held in the Department of Mathematics, University of Jammu, Jammu, India on February 25-27, 2011.
14. Presented a paper entitled “Pseudo Perfect modules” in the International Conference on Algebra and its Applications (ICAA-10) held in the Department of Mathematics, Aligarh Muslim University, Aligarh, India during February 20-22, 2010.

List of Delivered Lectures/Talks in the Workshop/University

1. Delivered an invited lecture (online mode) on “Basic Linear Algebra and its applications in Error correcting codes” in the Refresher courses in Mathematics and its Applications held at UGC-Malaviya Mission Teacher Training Cetre, University of Allahabad, Prayagraj, India during Nov 06, 2024 – Nov 19, 2024. 
2. Delivered two invited lectures (online mode) on “Algebraic structures and their applications in Error correcting codes” in the Refresher courses on Mathematical Sciences (Mathematics/ Statistics / Operational Research/ Computer Sciences)  held at Centre for Professional Development in Higher Education (CPDHE), University of Delhi, Delhi, India during 18th September 2024 – 1st October 2024. 
3. Delivered an Invited talk on "Overview of Algebra and Linear Codes" in the Workshop on Algebraic Codes & Magma Computation organized by IIT Patna, India during November 10-11, 2023 (online mode).
4. Delivered a lecture on ''Introduction to Coding Theory" in NIWC on Code-Based Cryptography organized by IIT-BHU, Varanasi, India during July 5-7, 2023.
5. Delivered two invited lectures (online mode) on “Semi-simple rings” in the Refresher courses on Maths, Statistics & Computer Science(MD) held at UGC-Human Resource Development Centre, University of Lucknow, Lucknow, India during January 10-23, 2023.  
6. Delivered a talk in the National workshop on “Latest Trends in Mathematics with their Applications” organized by the Department of Science and Humanities (Mathematics) at NIT Nagaland, India during December 11-15, 2017 under TEQIP-III.
7. Delivered a talk on “Error Correcting Codes” in the Department of Mathematics and Statistics, Gurukul Kangari Vishwavidyalaya, Haridwar during September 25-26, 2017.
8. Delivered a talk in the QIP short term workshop on “Algebra, Analysis and Applications” was held in the Department of Mathematical Sciences, IIT (BHU), Varanasi from 03 July-09 July 2017. 
9. Delivered two invited lectures on “System of Linear Equations and Rank of Matrices” in Advanced Training Programme in Linear Algebra and Analysis-2009 for Undergraduate Students held at the Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India during Nov 25-Dec 04, 2010.

List of Workshops Attended

1. National Instructional Workshop on Cryptology (NIWC-2015) held at Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla, (H.P.), India during 18-22 May, 2015.
2. National Instructional Workshop on Graph Theory and its Applications held at DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India during 23-28 May 2011.
3. Discussion Meeting on Finite Fields and Coding Theory organized at the Harish-Chandra Research Institute (HRI), Jhunsi, Allahabad, India during 02-14 November, 2009.