Professor

Department of Mathematics

Motilal Nehru National Institute of Technology Allahabad, Prayagraj, India-211004

E-mail: sdt[at]mnnit[dot]ac[dot]in

Telephone: +915322271252(O) +915322271606(R) 9452880914(M)

**Award and Honors:**- RESEARCH AWARDS/FELLOWSHIPS RECEIVED • Mathematics Research Fellowship at the Abdus Salam, International Centre For Theo- retical Physics, Trieste, Italy from May 18 to July 17, 2009. • Mathematics Research Fellowship at the Abdus Salam, International Centre For Theo- retical Physics, Trieste, Italy from May 18 to June 17, 2008. • Visiting Scientist at the Johann Radon Institute for Computational and Applied Math- ematics(RICAM), Linz, Austria from May 15, 2006 to June 15, 2006. • Mathematics Research Fellowship at the Abdus Salam, International Centre For Theo- retical Physics, Trieste, Italy from June 1, 2004 to September 2, 2004. • Junior and Senior Research Fellowships at Harish-Chandra Research Institute, Jhunsi, Allahabad in Commutative Algebra from 14th August, 1992 to 9th May, 1996. OTHER AWARDS, HONOURS & RECOGNITIONS: 1. Outstanding Scientist Award by VDGOOD International Scientists Awards in the category of Engineering, Sciences & Medicine during 17 -18 October, 2020 in Kolkata. 2. Expert Member, DRC (Doctoral Research Committee), Madan Mohan Malviya Technological University, Gorakhpur since 2019. 3. Dewang Mehta National Education Award-2017 for Best Professor in Mathematics (regional round) on 14th September, 2017 at Vivanta by Taj hotel, Lucknow by Dy Chief Minister on UP (Dr Dinesh Sharma). 4. Guest of Honour in the International Conference on Recent Advances in Engineering Science and Management, August 11-12, 2017 at Vindhya Institute of Technology & Science, Satna (MP). 5. Expert Member, Board of Studies of Mathematics for Dr APJ Abdul Kalam Technical University, Uttar Pradesh, Lucknow since January, 2016. 6. Chairman in parallel session of Algebra in the conference “International Congress of Math- ematicians′′ at Coex, Seoul, South Korea during August 13-21, 2014. 7. Edushine 2014 : Honoured by the United Group of Institutions for distinguished services in the academic world on June 07, 2014 at United Campus Allahabad. 8. Member, Board of Studies of Mathematics Department, Bundelkhand University, Jhansi during 2014-16. 9. Invited as a Judge in the Chhattisgarh Young Scientists Congress 2013 held at Govt Nagarjuna P.G. College of Science, Raipur during Feb 28- March 01, 2013. 10. Edushine 2012 : Honoured by the United Group of Institutions for distinguished services in the academic world on May 25, 2012 at United Campus Allahabad. 11. Member of selection boards for faculty of several universities, Ph.D. thesis examiners of several universities and institutions. 12. Received Best Teacher Award in Government P. G. College, Ramanagar (Nainital), Uttrakhand in 2004.

**Conferences/ Workshops/Symposium/ Short-term Courses Organized:**- Conference/Workshop organized : 1. Chairman of National Instructional Workshop on Cryptography (NIWC-2018) during June 6-10, 2018 at MNNIT, Allahabad (budget: Rs 4.91 Lakhs, Participants: 90) 2. Joint Organizing Secretary of “National Conference Application of Mathematics in Engineering and Sciences” (AMES-2014) during November 29-30, 2014 at MNNIT, Allahabad. 3. Organizing Secretary of National Instructional Workshop on Cryptology(NIWC-2014) during June 5-9, 2014 at MNNIT, Allahabad. 4. Chairman of the National Workshop “Optimization Techniques and their applications” (NWOTA- 2013) during June 5-11, 2013 (seven days) at MNNIT, Allahabad. 5. Convenor and Chairman of the National Conference “Advances in Mathematical Sciences” during October 5-7, 2012 (three days) at MNNIT, Allahabad. 6. Chairman and Coordinator of the Workshop on Course Curriculum development of M.Sc. (Math- ematics and Scientific Computing) and B. Tech. Mathematics Courses on March 24, 2012. 7. Joint Secretary of the National Conference on “Application of Material Science in the Service of Society” at C M P Degree College, Allahabad in February 5-6, 2008. 8. Convenor of Workshop on Course Curriculum development of M.Sc. (Mathematics and Scientific Computing) in April, 2007.

**Projects Completed:**- RESEARCH PROJECTS: 1. National Board of Higher Mathematics sanctioned a research project entitled “Study of Rees Algebra, graded rings in module theoretic setup and its applications” of Rs 10,71,449/- for four years. Duration- April 01, 2010 to March 31, 2014 Status- Completed. 2. DST (Department of Science and Technology), Govt of India, sanctioned a research project ”Graded modules over rings graded by finitely generated Abelian groups” in 2011 of Rs 10,04,640/- for three years. Duration- December 12, 2011 to December 11, 2014 (file no. SR/S4/MS:642/10- 11) Status- Completed

**Expert Lectures:**- INVITED TALKS/SEMINARS 1. Delivered lecture on ”Representation Theory of Finite Groups” as a resource person at National Level 05 days Faculty Development Programme on Emerging Trends in Mathematics,Tirumala Engineering College, Jonnalagadda, Guntur Dristrict, Andhra Pradesh on 17/06/2021. 2. DeliveredInvitedtalkonNationalMathematicsDayatCSJMKanpurUniversityon′′Mathematical Models in Technology and Glimpse of Vedic Mathematics′′ on 22/12/2020. 3. Invited talk on ′′Algebraic and Differential Models in Engineering and Cryptography′′ in the workshop on ”Applications of Algebra in Science and Engineering (AASE-2020)′′, at National Institute of Technology, Jamshedpur on 12/10/2020. 4. Invited talk at Virtual Workshop on ′′Collating Mathematics Resources for Teachers in Higher Education”, by National Institute for Educational Planning and Administration, New Delhi on 06/10/2020 entitled Content and reading resources of Commutative Algebra, Group Theory and Differential Geometry (as a Resource Person). 5. Delivered two invited online webinar talks on “Mathematical Modeling in Technology′′ and “ Mathematical Modelling in Cryptography′′ on 9th July and 10th July, 2020. organized by Insti- tute of Engineering and Technology Lucknow. 6. Delivered an invited online webinar talk on “Applications of Mathematics in Engineering′′ on 27th May, 2020 organized by IIMT Greater Noida. 7. Delivered an invited talk “On Symbolic Rees Algebra of Modules′′ during December 20-22, 2019 at Mohanlal Sukhadiya University, Udaipur, Rajasthan in an International Conference on Recent Advances in Algebra, Analysis and Applications. 8. Delivered an invited talk in a DST INSPIRE programme on “Important concepts of Number Theory with Applications′′ on 14th November, 2019 at Savitri Mahavidyalay, Sonai, Karchhana, Prayagraj. 9. Delivered an invited talk in the DST sponsored programme ′′INSPIRE Science Camp′′ on 28th April, 2019 at Prayag Institute of Technology and Management , Bendo, Karchhana, Allahabad 10. Delivered an invited talk on ′′Geometric Invariant in the theory of D-modules′′ in the Asia Australia Algebra Conference held at Western Sydney University, Sydney, Australia from 21st January to 25th January, 2019. 11. Delivered an invited talk on “Applications of Mathematics in Present Technology” in CONIAPSXXIII at Kathmandu, Nepal during November 16-18, 2018. 12. Delivered two invited talks on “Mathematical ideas and their applications′′ during December 24- 25, 2017 at Kendriya Vidyalay Old Cantt, Allahabad in a TGT Mathematics Teachers training programme. 13. Delivered two invited talks on “Rational and Jordon Canonical forms′′ and “Grobner basis and its applications′′ during December 12-13, 2017 in a National Workshop LTMTA-2017 at National Institute of Technology, Nagaland, Dimapur. 14. Delivered invited talk on KVPY and Mathematics Olympiad: Ideas & Methods in Mathematics and its applications on May 18-19, 2017 at Kendriya Vidyalay Old Cantt, Allahabad to TGT Mathematics Teachers. 15. Delivered Invited plenary talk on “Some Applications of Mathematics in Today’s Technology′′ in the National conference ”Recent Trends in Mathematical Sciences” (NCRTMS-16) at Madan Mohan Malviya Technical University, Gorakhpur during 12-13 April, 2016. 16. Delivered invited talk “Integrability theorem for Weyl Algebra and its relation with Heisenberg uncertainty principle” in international conference of “Infinite and finite dimensional complex analysis and its applications′′ at Anand International College of Engineering Jaipur during Aug 22-25, 2016. 17. Delivered Invited talk on “An Elementary Approach to Ideas & Methods in Mathematics and its Applications′′ on February 18, 2016 in the “Motivational Science Learning Camp” at CMDR, MNNIT, Allahabad during 17-21 February, 2015. 18. Delivered Invited talk on ′′Mathematics behind present technology“ and Chaired a session in the National conference on ′′ Mathematical and Statistical Techniques and their Applications to Science and Engineering“ during November 20-21, 2015 at DIT University Dehradun. 19. Gave invited talk on “Coisotropic property of characteristic variety and its relation with Heisen- berg uncertainty principle in the national conference on Commutative Algebra and Algebraic Geometry at IIT, Guwahati during February 5 - 9, 2015. 20. Gave an invited talk on “Algebraic Foundations of Cryptography: Finite Fields” National In- structional Workshop on Cryptology (NIWC-2014) during June 5-9, 2014 at MNNIT, Allahabad. 21. Invited talks (four lectures) on ′′Nilpotent groups and field extensions“ at Nagarjuna Govt. P.G. College of Science, Raipur(Chhattisgarh) during August 28-29, 2013. 22. Gave a talk on ′′Game Theory′′ in the National Workshop on “Optimization Techniques and their applications” (NWOTA-2013) during June 5-11, 2013 at MNNIT, Allahabad. 23. Invited talk on “Applications of Mathematics and Cryptography” as a resource person in a training programme/workshop of HRD Ministry, Hindi Shabdawali Ayog, at Karm Kshetra P. G. College, Etawa on February 27, 2013. 24. Gave an invited talk on “The coisotropic variety of Weyl algebra” in the national conference on ′′Recent Advances in Mathematics”, at Rani Durgavati University, Jabalpur January 14, 2013. 25. Invited talks on “Projective modules and unimodular rows” in the national conference on ′′ Anal- ysis and its applications”, at National Institute of Technology, Srinagar (J&K) during November 19-20, 2012. 26. Twoinvitedtalkson“BoundaryvalueproblemsoveranIntegro-DifferentialAlgebra”and“Cryptosystem based on platform group of amalgamated free products of braid group and Thompson group” in an International conference on ′′Application of Computer Algebra”, at Sofia, Bulgaria during June 25-28, 2012. 27. Invited talk on “Braid group and Thomson group based Cryptosystem” in an International conference on ′′Group Theory and Lie Theory”, at Harish-Chandra Research Institute, Allahabad during March 19-21, 2012. 28. Delivered an invited talk on “Cryptosystem based on braid group and Thomson group” in a National workshop on ′′Recent trends in Graph Theory and Cryptography“, at Govt VYT PG Autonomous College, Durg (Chhattisgarh) on October 13, 2011. 29. Invited talk on “Applications of Mathematics and Cryptography” as a resource person in a training programme/workshop of HRD Ministry, Hindi Shabdawali Ayog, at Janata Degree College, Bakewar, Etawa on September 30, 2011. 30. Invited talks (seven lectures) as a resource person in a DST workshop (UGTPM) in IIT, Patna during May 15-20, 2011. 31. Gave invited talk as a resource person on “Cryptography and Importance of Mathematics“ in a national workshop of HRD Ministry, Hindi Shabdawali Ayog, on March 03, 2011 at Vivekanand P.G. College, Dibiyapur, Oraiya. 32. Invited talk on “Braid and transversal based crypto system′′ in the CIMPA-Vietnam school on “Braids in Algebra, Topology and Geometry′′ at the Institute of Mathematics, Hanoi, Vietnam during January 17-28, 2011. 33. Two invited talks as a resource person in the UGC Sponsored National Workshop on ′′Emerging of applications of Mathematics′′ in B.C.S. Government P.G. College, Dhamtari, Chhattisgarh during October 27 -28, 2010 one on ′′Representations of finite groups′′ and another on ′′ ′′ Finite field extensions and Galois theory . 34. Presented research paper ′′Analogue of Eakin Sathaye Theorem over Rees Algebra′′ in the Inter- national Congress of Mathematicians, Hyderabad, during August 19-27, 2010. 35. ”Projective Modules and completion of an unimodular row to an elementary matrix”, Indian Mathematical Society Conference at Allahabad University, Allahabad, during December 27-30, 2008. 36. A talk on “Homotopy of Sections of Ideals over a Noetherian ring” in the School and Conference on Algebraic K-Theory and its Applications (May 14 - June 1, 2007) at the Abdus Salam, International Centre For Theoretical Physics, Trieste, Italy. 37. Invited talk on the “Sections of zero dimensional ideals over a Noetherian ring ” at the CIMPA- UNESCO- Spain School from on 14-21 August, 2006 at Universidad Complutense de Madrid, Madrid, Spain. 38. Talk on the topic “Projective modules and generators of an ideal over Noetherian rings” at Allahabad University in Feb, 2005. 39. Gave a seminar on the topic “Sections of projective modules and a question of Nori” at the The Abdus Salam, International Centre For Theoretical Physics, Trieste, Italy on 27th August, 2004. 40. Invited talk on the topic “Projective generation of ideals” at the national seminar organized by Jammu Mathematical Society and Dept. of Mathematics, Jammu University from 20-22 February, 2004. 41. A talk on the topic “Generators of ideals” at the University of Allahabad in June, 2001. 42. Presented a paper entitled “Lifting of generators of ideals over a Noetherian ring” presented in the national level conference at Aligarh Muslim University in March, 2001. 43. Talk on the topic “Homotopy sections of projective modules over a Laurent polynomial ring” at Harish Chandra Research Institute, Allahabad in June, 2000.

**Other Significant Achievements:**- MEMBER OF EDITORIAL BOARD OF THE JOURNALS 1. International Journal of Engineering and Applied Sciences since January 2013. 2. American Journal of Applied Mathematics and Statistics, since 2013 (SCIEP). 3. Applied Mathematics and Sciences: An International Journal (MathSJ ) REVIEWER OF INTERNATIONAL JOURNALS AND BOOKS: 1. National Academy of Science Letters, National Academy of Sciences, 04/2020 2. Computational Methods for Differential Equations University of Tabriz 09/2020 3. Journal of Prime Research in Mathematics, Abdus Salam School of Mathematical Sciences, GC University, 06/2021 4. Journal of Scientific Research, BHU (On reduction and relation type of an ideal) Banaras Hindu University, 06/2021 5. Mathematical Reviews/MathSciNet, American Mathematical Society, USA (Reviewer num- ber: 098594). 6. Communications in Algebra, Taylor & Francis Publication, SCI Journal. 7. Springer Plus, SCI Journal 8. Journal of Indian Mathematical Society 9. Annals of Fuzzy Mathematics and Informatics 10. Science Journal of Applied Mathematics and Statistics, Science PG. 11. International Journal of Engineering, science & Technology(IJEST) 12. Turkish Journal of Mathematics, published from Ankara, Turkey. 13. International Journal of Information Technology & Decision Making. 14. “Higher Engineering Mathematics′′ of Pearson Education Publication, New Delhi
- FOREIGN COUNTRY VISITED FOR ACADEMIC PURPOSE 1. Italy- 2004, 2006, 2008, 2009- The Abdus Slam International Centre for Theoretical Physics, Trieste 2. Iran-2005- Institute for Advanced Studies In Basic Sciences, Zanjan 3. Spain -2005- Universidad Complutense de Madrid 4. Austria - 2006 - RICAM, Linz 5. Turkey - 2008- Istambul 6. Vietnam - 2011- Institute of Mathematics, Hanoi 7. Singapore - 2011 8. Bulgaria - 2012 - Sofia 9. Germany - 2013 - University of Osnabrueck 10. South Korea - 2014 - ICM, COEX, Seoul 11. Brazil - 2018 - Riocentro, Rio de janeiro 12. Nepal - 2018 - NAST, Kathmandu 13. Australia - 2019 -Western Sydney University, Sydney