## Rajat Kanti Nath

Designation :Assistant Professor.

Qualification :M.Sc. (Tezpur University), M.Phil.,Ph.D. (North-Eastern Hill University).

Specialization :Finite group theory and character theory of finite groups.

Title of the M. Phil. Thesis:Commutativity Degree of Finite Groups- A Survey.

Title of the Ph. D. Thesis :Commutativity Degree, its Generalizations, and Classification of Finite Groups.

Name of the Supervisor:Prof. Ashish Kumar Das.

Date of Joining TU :17 August, 2011.

Details of Employment:

(3) 17th August, 2011 to present: Assistant Professor, Department of Mathematical Sciences, Tezpur University, Assam.

(2) 14th February, 2011 to 6th August, 2011: Post Doctoral Fellow in Mathematics, Harish-Chandra Research Institute, Allahabad.

(1) 26th July, 2010 to 31st January, 2011: Assistant Professor, Department of Basic Sciences, DBCET, Assam Don Bosco University, Assam.

Current Research Scholar:

Name:Mr. Parama Dutta

Area of work:Generalized commuting probabilities of some finite algebraic structures.

List of Publications:

(34) J. Dutta, D. K. Basnet and R. K. Nath, Commuting probabilities of n-centralizer finite rings, submitted for publication.

(33) P. Dutta and R. K. Nath, Various energies of commuting graphs of some super integral groups, submitted for publication.

(32) P. Dutta and R. K. Nath, Some bounds for relative autocommutativity degree, submitted for publication.

(31) P. Dutta and R. K. Nath, On generalized commuting probability of finite rings, submitted for publication.

(30) P. Dutta and R. K. Nath, Autocommuting probability of a subgroup relative to another subgroup, submitted for publication.

(29) R. K. Nath, On asymptotic commutativity degree of finite groups, submitted for publication.

(28) J. Dutta and R. K. Nath, Spectrum and genus of commuting graphs of some classes of finite rings, submitted for publication.

(27) J. Dutta, D. K. Basnet and R. K. Nath, Characterizing some rings of finite order, submitted for publication.

(26) P. Dutta and R. K. Nath, On relative commuting probability of finite rings, under revision.

(25) R. K. Nath and S. K. Prajapati, On the number of solutions of a generalized commutator equation in finite groups,Acta Mathematica Hungarica, accepted for publication.

(24) R. K. Nath, A note on super integral rings,Boletim da Sociedade Paranaense de Matemática, accepted for publication.

(23) P. Dutta and R. K. Nath, On generalized autocommutativity degree of finite groups,Hacettepe Journal of Mathematics and Statistics, accepted for publication.

(22) J. Dutta, D. K. Basnet and R. K. Nath, A note on n-centralizer finite rings,An. Stiint. Univ. Al. I. Cuza Iasi Mat., accepted for publication.

(21) P. Dutta and R. K. Nath, On Laplacian energy of non-commuting graphs of finite groups,Journal of Linear and Topological Algebra, 7 (2018), no. 2, 121–132.

(20) P. Dutta, J. Dutta and R. K. Nath, On Laplacian spectrum of non-commuting graph of finite groups,Indian Journal of Pure and Applied Mathematics, 49 (2018), no. 2, 205–216.

(19) P. Dutta and R. K. Nath, Autocommuting probability of a finite group,Communications in Algebra, 46 (2018), no. 3, 961–969.

(18) P. Dutta and R. K. Nath, A generalization of commuting probability of finite rings,Asian-European Journal of Mathematics, 11 (2018), no. 2, 1850023 (15 pages).

(17) R. K. Nath, Various spectra of commuting graphs of n-centralizer finite groups,International Journal of Engineering, Science and Technology, 10 (2018), no. 2S, 170–172.

(16) J. Dutta and R. K. Nath, Laplacian and signless Laplacian spectrum of commuting graphs of finite groups,Khayyam Journal of Mathematics, 4 (2018), no. 1, 77–87.

(15) J. Dutta, D. K. Basnet and R. K. Nath, On generalized non-commuting graph of a finite ring,Algebra Colloquium, 25 (2018), no. 1, 149–160.

(14) J. Dutta and R. K. Nath, Finite groups whose commuting graphs are integral,Matematicki Vesnik, 69 (2017), no. 3, 226–230.

(13) J. Dutta, D. K. Basnet and R. K. Nath, On commuting probability of finite rings,Indagationes Mathematicae, 28 (2017), no. 2, 372–382.

(12) J. Dutta and R. K. Nath, Spectrum of commuting graphs of some classes of finite groups,Matematika, 33 (2017), no. 1, 87–95.

(11) R. K. Nath and M. K. Yadav, On the probability distribution associated to commutator word map in finite groups,International Journal of Algebra and Computation, 25 (2015), no. 7, 1107–1124.

(10) R. K. Nath and M. K. Yadav, Some results on relative commutativity degree,Rendiconti del Circolo Mathematico di Palermo, 64 (2015), no. 2, 229–239.

(9) R. K. Nath, A new class of almost measure preserving maps on finite simple groups,Journal of Algebra and its application13 (2014), no. 4, 1350142 (5 pages).

(8) R. K. Nath, Commutativity degree of a class of finite groups and consequences,Bulletin of Australian Mathematical Society, 88 (2013), no. 3, 448–452.

(7) A. K. Das, R. K. Nath and M. R. Pournaki, A survey on the estimation of commutativity in finite groups,Southeast Asian Bulletin of Mathematics, 37 (2013), no. 2, 161–180.

(6) A. K. Das and R. K. Nath, A generalization of commutativity degree of finite group,Communications in Algebra, 40 (2012), no. 6, 1974–1981.

(5) R. K. Nath and A. K. Das, On generalized commutativity degree of a finite group,Rocky Mountain Journal of Mathematics, 41 (2011), no. 6, 1987–2000.

(4) A. K. Das and R. K. Nath, A characterization of certain finite groups of odd order,Mathematical Proceedings of the Royal Irish Academy, IIIA (2011), no. 2, 69–78.

(3) R. K. Nath and A. K. Das, On a lower bound of commutativity degree,Rendiconti del Circolo Mathematico di Palermo, 59 (2010), no. 1, 137–141.

(2) A. K. Das and R. K. Nath, On generalized relative commutativity degree of a finite group,International Electronic Journal of Algebra, 7 (2010), 140–151.

(1) A. K. Das and R. K. Nath, On Solutions of a class of equations in a finite group,Communications in Algebra, 37 (2009), no. 11, 3904–3911.

Book Published:

(1) Some new directions in Commutativity Degree of finite groups: Recent Developments, LAP LAMBERT Academic Publishing House, Germany, 2011, ISBN No. 978-3-8465-4657-4.

Selected talks:

(6)Necessity of thinking and imagination in learning Mathematicsdelivered in the Teachers’ Orientation Programme on June 27, 2017, MVMSS School, Guwahati.

(5)A series of four lectures on group theorydelivered in the Instructional school 2013 on Group Theory and Linear Algebra, December 17 to 20, 2013, Centre for Applied Mathematics, Central University of Jharkhand, Ranchi.

(4)Commuting probability on finite groupsdelivered in Department of Mathematics, D.H.S.K. College, Dibrugarh on September 21, 2013.

(3)On generalized commutativity degree of finite groupsdelivered in the International Conference on Group Theory and Lie Theory, March 19 to 21, 2012, Harish-Chandra Research Institute, Allahabad.

(2)On commutativity degree of finite groupsdelivered in the Workshop on Algebra and Number Theory, December 22 to 26, 2010, Tezpur University.

(1)Commutativity degree, its generalizations, and classification of finite groupsdelivered in the International Conference on Groups, Actions and Computations, September 10 to 12, 2010, Harish-Chandra Research Institute, Allahabad.

Conference/ School/ Workshop Attended:

(32) International Conference on Discrete Mathematics and its Application to Network Science, held at the Department of Mathematics, BITS Pilani, K. K. Birla Goa Campus from July 7 to 10, 2018.

(31) Workshop on UGC guidelines of Career Advancement Scheme, organized by IQAC, Tezpur University on June 13, 2018.

(30) Workshop on Revised Framework of NAAC Accreditation, organized by IQAC, Tezpur University on May 4, 2018.

(29) Workshop on Cyber Security: Issues and Challenges, held at Dept. of Computer Science and Engineering, Tezpur University, conducted by Dept. of Computer Science and Engineering, Tezpur University from January 29 to 30, 2018.

(28) National Conference on Advances in Sciences, Engineering and Technology held at GIMT Tezpur, organized by GIMT Tezpur from November 10 to 11, 2017.

(27) Pedagogy for Online and Blended Teaching-Learning Process, held at Tezpur University, conducted by IIT Bombay from September 14 to October 12, 2017.

(26) Foundation Program in ICT for Education, held at Tezpur University, conducted by IIT Bombay from August 03 to September 7, 2017.

(25) 112th Orientation Programme, UGC-HRDC, Gauhati University, from May 29 to June 25, 2017.

(24) National Seminar on Science and Technology for Human Welfare, held at Institute of Advanced Study in Science and Technology (IASST), Guwahati, organized by IASST, Guwahati on February 27, 2017.

(23) National Conference on Advances in Mathematical Sciences, held at Gauhati University, organized by Department of Mathematics, Gauhati University from December 22 to 23, 2016.

(22) National Conference on Mathematics and its Applications, held at Cotton College, organized by the Department of Mathematics, Cotton College and Cotton College State University from October 21 to 22, 2016.

(21) School on Analysis and Topology, held at ISI North East Centre, organized by ISI North East Centre and Tezpur University from February 22 to March 04, 2016.

(20) Two-week ISTE STTP on Technical Communication, held at Tezpur University, conducted by IIT Bombay from October 08 to December 05, 2015.

(19) Seminar on Work and Achievement of Prof. Manjul Bhargava: Fields Medalist 2014, organized by Department of Mathematical Sciences, Tezpur University on September 06, 2014.

(18) Workshop on Credit Based Academic System, organized by IQAC, Tezpur University on June 19, 2014.

(17) Workshop on Quality Teaching, organized by IQAC, Tezpur University on July 26, 2012.

(16) International Conference on Group Theory and Lie Theory, held at Harish-Chandra Research Institute, Allahabad, organized by Harish-Chandra Research Institute from March 19 to 21, 2012.

(15) Workshop on Question Paper Setting and API, organized by IQAC, Tezpur University on March 14 to 15, 2012.

(14) Workshop on Analysis, held at Tezpur University, organized by Indian Statistical Institute, Kolkata, and Department of Mathematical Sciences, Tezpur University, January 3 to 9, 2012.

(13) Advanced Training in Mathematics School on Workshop in Group Theory held at Indian Institute of Science Education and Research Mohali. Organized by National Board of Higher Mathematics, India, from 16th May to 21st May, 2011.

(12) International Conference on Group, Action and Computations held at Harish-Chandra Research Institute, Allahabad, organized by International centre for theoretical sciences, Mumbai, from September 10 to 12, 2010.

(11) Professional Enrichment Programme: Interactive Teaching held at Don Bosco College of Engineering and Technology, organized by Assam Don Bosco University, Guwahati, from September 3 to 4, 2010.

(10) UGC-SAP workshop on Algebra, Algebraic Topology and related topics, held at North-Eastern Hill University, Meghalaya, organized by Dept. of Mathematics, NEHU, Meghalaya, from March 15 to 20, 2010.

(9) National Conference on Recent Trends in Mathematics and its Applications, held at Gauhati University, organized by Assam Science Society and Gauhati University, Assam, India, from September 12 to 13, 2009.

(8) Advanced Instructional School in Mathematics on COMBINATORICS & GRAPH THOERY (AIS-CGT), held at Bhaskaracharya Pratishthana, Pune, India. Organized by National Board of Higher Mathematics, India, from 8 May to 4 June, 2009.

(7) Short term visits: Tata Institute of Fundamental Research (TIFR, Mumbai), from June 4 to 12, 2009.

(6) 96th Indian science Congress, held at North-Eastern Hill University, Meghalaya, India. Organized by The Indian Science Congress Association, from January 3 to 7, 2009.

(5) International Workshop and Conference on Surface Mapping Class Groups and Related Topics, held at North-Eastern Hill University, Meghalaya, India. Organized by Department of Mathematics, North-Eastern Hill University, Meghalaya, India, from June 16 to 28, 2008.

(4) CMFT Workshop, 2008, held at Don Bosco Institute, Guwahati, India. Organized by CMFT, Germany, from January 3 to 10, 2008.

(3) Advanced Instructional School in Mathematics on ALGEBRAIC AND ANALYTIC NUMBER THEORY, held at Harish-Chandra Research Institute, Allahabad, India. Organized by National Board of Higher Mathematics, India, from December 3 to 28, 2007.

(2) North-East School on Computational Geometry, held at St. Anthony's College, Meghalaya, India. Organized by Advanced computing & Microelectronics Unit, Indian Statistical Institute, Kolkata, and Department of Computer Science, St. Anthony's College, Meghalaya, India, from November 1 to 3, 2007.

(1) Symposium on Some Recent Advances in Mathematics, held at North-Eastern Hill University, Meghalaya, India. Organized by Department of Mathematics, North-Eastern Hill University, Meghalaya, India, from April 4 to 5, 2007.

Papers Presented:

(8)Relative r-noncommuting graph of a finite ring, presented in the International Conference on Discrete Mathematics and its Application to Network Science, held at the Department of Mathematics, BITS Pilani, K. K. Birla Goa Campus from July 7 to 10, 2018.

(7)Various spectra of commuting graphs of n-centralizer finite groups, presented in the National Conference on Advances in Sciences, Engineering and Technology held at GIMT Tezpur, organized by GIMT Tezpur from November 10 to 11, 2017.

(6)Spectral aspects of commuting graphs of n-centralizer finite groups, presented in the National Seminar on Science and Technology for Human Welfare, held at Institute of Advanced Study in Science and Technology (IASST), Guwahati, organized by IASST, Guwahati on February 27, 2017.

(5)On super integral rings, presented in the National Conference on Advances in Mathematical Sciences, held at Gauhati University, organized by Department of Mathematics, Gauhati University from December 22 to 23, 2016.

(4)On a problem posed by Paul Lescot, presented in the National Conference on Mathematics and its Applications, held at Cotton College, organized by the Department of Mathematics, Cotton College and Cotton College State University from October 21 to 22, 2016.

(3)On a lower bound of commutativity degree, presented in the UGC-SAP Workshop on Algebra, Algebraic Topology and Related topics, held at North-Eastern Hill University, Meghalaya, organized by the Department of Mathematics, North-Eastern Hill University, Meghalaya, from March 15 to 20, 2010

(2)Some generalizations of commutativity degree and classifications of finite groups, presented in the National Conference on Recent Trends in Mathematics and its Applications, held at Gauhati University, organized by Assam Science Society and Gauhati University, Assam, India, during September 12 to 13, 2009

(1)Certain generalizations of commutativity degree of finite groups, presented in the 96th Indian science Congress, held at North-Eastern Hill University, Meghalaya, India. Organized by The Indian Science Congress Association, during January 3 to 7, 2009.

Reviewing experience:

Working as reviewer ofMathematical Reviews.Worked as a referee of following journals:

(10) Discrete Mathematics, Algorithms and Applications

(9) Communications in Algebra

(8) Hacettepe Journal of Mathematics and Statistics

(7) Publicationes Mathematicae Debrecen

(6) Proceedings - Mathematical Sciences

(5) ScienceAsia

(4) International Electronic Journal of Algebra

(3) Journal of Group Theory

(2) Ars Combinatoria, a Canadian Journal of Combinatorics

(1) Graph and Combinatorics.Last updated on July 23, 2018.

Awards and achievements:

(4) Biographical profile published in Marquis Who's Who in the world 2013 (30th Pearl Anniversary Edition)

(3) Post Doctoral Fellowship at Harish-Chandra Research Institute, Allahabad for the year 2011.

(2) Certificate of Appreciation by Government of India, Ministry of Human Resource Development to witness the Republic Day Parade, 2007 from the Prime Minister's Box at Rajpath, New Delhi as a guest of hon'ble Prime Minister of India.

(1) Gold Medal for securing the first position in M. Sc.(Mathematics), Tezpur University in the year 2006.