NISER

• Ph.D.: Harish-Chandra Research Institute, Prayagraj, India.
• M.Sc.: Chennai Mathematical Institute, Chennai, India.
• B.Sc.: Institute of Mathematics and Applications, Bhubaneswar, India.

Algebra (Group Theory and Related Topics)

• NBHM Post Doctoral Fellowship, 2020.
• Institute Post Doctoral Fellowship at IISER Mohali, October 2018.
• HRI-INFOSYS AWARD for excellence in research in Group Theory, 2018.
• DAE Fellowship for PhD Program at the Harish-Chandra Research Institute, 2013.
• NBHM PhD Scholarship, 2013 (did not avail).

1. Neeraj Kumar Dhanwani, Pravin Kumar, Tushar Kanta Naik, and Mahender Singh, Linearity, crystallographic quotients, and automorphisms of virtual Artin groups, Submitted, https://arxiv.org/abs/2409.10270.
2. Pravin Kumar, Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups, Journal of Pure and Applied Algebra, 228 (2024), no. 11, Paper No. 107713, 27 pp.
3. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Virtual twin groups and permutations, J. Group Theory, 27 (3), 2024, 443-483
4. Pravin Kumar, Tushar Kanta Naik, and Mahender Singh, Congruence subgroups and crystallographic quotients of small Coxeter groups, Forum Mathematicum, 36(1), 2024, 193-213.
5. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Structure and automorphisms of pure virtual twin groups, 2023, Monatsh. Math., 202 (3), 2023, 555 – 582.
6. Rijubrata Kundu, Tushar Kanta Naik, and Anupam Singh, Nilpotent Lie algebras with two centralizer dimensions over a finite field, Journal of Algebra, 633, 2023, 362-388.
7. Rijubrata Kundu, Tushar Kanta Naik, and Anupam Singh, Nilpotent Lie algebras of breadth type (0, 3), Communications in Algebra, 51 (9), 2023, 3792 – 3809.
8. Tushar Kanta Naik, and Mahender Singh, Automorphisms of odd Coxeter groups, Monatsh. Math., 195 (3), 2021, 501 – 521.
9. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Some remarks on twin groups, J. Knot Theory Ramifications, 29 (10), 2020, 2042006, 14 pp.
10. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Conjugacy classes and automorphisms of twin groups, Forum Math., 32 (5), 2020, 1095 – 1108.
11. Tushar Kanta Naik, Rahul Dattatraya Kitture, and Manoj K. Yadav, Finite p-groups of nilpotency class 3 with two conjugacy class sizes, Israel J. Math., 236 (2), 2020, 899 – 930.
12. Tushar Kanta Naik, On the probability distribution associated to commutator word map in finite groups, Communications in Algebra, 47 (9), 2019, 3808 – 3817.
13. Tushar Kanta Naik, and Manoj K. Yadav, Finite p-groups of conjugate type {1, p³}, J. Group Theory, 21 (1), 2018, 65 – 82.

1. Finite group theory: Classification of finite p-groups, Influence of conjugacy class sizes on the structure of finite groups, Automorphisms of finite groups, Word maps defined on groups, Graphs associated with groups.
2. Combinatorial group theory / Low dimensional topology: Coxeter groups and Artin groups, Braid groups, Planar braid groups, their virtual analogous and pure subgroups.
3. (Nilpotent) Lie algebra: Classification of finite dimensional nilpotent Lie algebras, Camina Lie algebras, Breadth of a Lie algebra.

Current:

Master Thesis (Int. M. Sc. Student, NISER)

1. Aarjav Jogani (2024 - 2025)

Master Thesis (Int. M. Sc.-Ph.D. Student, NISER)

1. Arijit Mahato (2024 - 2025)

Past:

Post Doctoral Fellow:

1. Rohit Garg (July 2023 - July 2024).

One-Semester Projects (NISER Students):

1. Arijit Mahato (Int. Ph.D.), Fall 2023, Spring 2024.
2. Saheli Panja (Int. Ph.D.), Fall 2023.
3. Prasaman Ghosh (Int. M.Sc.), Fall 2023.

Summer Projects:

1. Aarjav Jogani (Braid groups), NISER, June-July, 2024.
2. Aditya Vikram Saraf (Free Product and Ping-pong Lemma), NISER, June-July 2024.
3. Muskan Choudhary (Combinatorial and Geometric group theory), IISER Bhopal, May-July 2024.
4. Krishna Dhrua (Symmetric Groups), NIT Rourkela, May-July 2024.
5. Tulasi Behera (Groups of small order), NIT Rourkela, May-July 2023.
6. Rameswar Patro (Combinatorial aspects of Coxeter groups), NISER, May-July 2023.

• Field Theory (M307, MA806): Int. M.Sc. + Int. Ph.D., NISER, Spring 2025.
• Algebra I (MAT 601): Ph.D., NISER, Fall 2024.
• Group Theory (M202): Int. M.Sc., NISER, Spring 2024.
• Topology (M405, MA803): Int. M.Sc. + Int. Ph.D., NISER, Fall 2023.
• Metric Spaces (M204): Int. M.Sc., NISER, Spring 2023.
• Mathematical Analysis (MA702): Int. Ph.D.,  NISER, Fall 2022.

Teaching at Conferences/Workshops/Outreach Programs

• Extra-Mural Lecture on Exploring the beauty of Group theory, Sundargarh Govt. College, 19th February, 2024
• High-School Algebra, Rural Mathematics Talent Search Program, Dungripali High School, Sonepur, Odisha, December 2023.
• Combinatorial Group Theory,  Workshop on Group Theory and Around, HRI, December 2023.
• Number Theory: SOPM, NISER, May-June 2023

1. Member, Selection Committee for Int. M.Sc. - Ph.D. Program, SMS, NISER, 2023 and 2024. 
2. Member, Screening Committee for shortlisting Ph.D applications, SMS, NISER, 2024.
3. Member, Ph.D. Monitoring Committee, SMS, 2023.
4. Member, UGCS, SMS, NISER, 2022 - till date.
5. Convener, SMS (School of Mathematical Sciences, NISER) Website, (2022 - till date).