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. Arijit Mahato, Tushar Kanta Naik, A. Rameswar Patro, Symmetry and Rigidity of Star-Shaped Coxeter Systems, Submitted, https://arxiv.org/abs/2605.22065, Accepted for publication in Monatsh. Math.
3. 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.
4. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Virtual twin groups and permutations, J. Group Theory, 27 (3), 2024, 443-483
5. Pravin Kumar, Tushar Kanta Naik, and Mahender Singh, Congruence subgroups and crystallographic quotients of small Coxeter groups, Forum Mathematicum, 36(1), 2024, 193-213.
6. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Structure and automorphisms of pure virtual twin groups, 2023, Monatsh. Math., 202 (3), 2023, 555 – 582.
7. 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.
8. Rijubrata Kundu, Tushar Kanta Naik, and Anupam Singh, Nilpotent Lie algebras of breadth type (0, 3), Communications in Algebra, 51 (9), 2023, 3792 – 3809.
9. Tushar Kanta Naik, and Mahender Singh, Automorphisms of odd Coxeter groups, Monatsh. Math., 195 (3), 2021, 501 – 521.
10. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Some remarks on twin groups, J. Knot Theory Ramifications, 29 (10), 2020, 2042006, 14 pp.
11. Tushar Kanta Naik, Neha Nanda, and Mahender Singh, Conjugacy classes and automorphisms of twin groups, Forum Math., 32 (5), 2020, 1095 – 1108.
12. 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.
13. Tushar Kanta Naik, On the probability distribution associated to commutator word map in finite groups, Communications in Algebra, 47 (9), 2019, 3808 – 3817.
14. 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.

Ph.D. Thesis  (Ongoing)

1. Arijit Mahato (To be completed in 2029)

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

1. An Introduction to Chevalley Groups, A. Rameswar Patro, 2025 - 2026.
2. Braids, Knots, and Links, Aarjav Jogani, 2024 - 2025. Received the Best Thesis Award.

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

1. Combinatorial Aspects of Coxeter Groups and Related Structures, Arijit Mahato, 2024 - 2025. Received the Best Thesis Award.

Post Doctoral Fellow:

1. Rahul Kaushik (April 2025 - April 2026).
2. Rohit Garg (July 2023 - July 2024).

One-Semester Projects (NISER):

Int. M. Sc.-Ph.D.

1. Lakshmi Kalyanaraman, Fall 2026.
2. Ananya Khutia, Fall 2025, Spring 2026.
3. Pooja Patel,       Fall 2025, Spring 2026.
4. Ananta Sabata, Fall 2025.
5. Arijit Mahato,    Fall 2023, Spring 2024.
6. Saheli Panja,     Fall 2023.

Int. M. Sc.:

1. Prasaman Ghosh (Int. M.Sc.), Fall 2023.

Summer Internship (May -July):

2026

1. Coxeter Groups, Arpita Sahoo, IISER Bhopal.

2025

1. Dihedral Groups, Ashrita Satapathy, IMA Bhubaneswar.
2. Homomorphism between Symmetric groups, Manisha Panda, IMA Bhubaneswar.
3. Groups of prime power orders, Priyabrata Sandha, Sambalpur University.

2024

1. Combinatorial and Geometric group theory, Muskan Choudhary, IISER Bhopal.
2. Symmetric Groups, Krishna Dhrua, NIT Rourkela.

2023

1. Groups of small order, Tulasi Behera, NIT Rourkela.

NISER Students

2026

1. Anitya Bibhab Sri.
2. Centralizers in Symmetric Groups and Wreath Product, Divyanshu Singh.
3. Dihedral Groups, Ethan Savio Coutinho.
4. Group Actions, Hitesh Chauhan.
5. Semi-direct Products, Lavish Meena.
6. Introduction to Free Groups, Shailesh.
7. Automorphisms, Udayveer.
8. Cayley Graph, Yash Ojha.

2025

1. Word Maps on Groups, A. Rameswar Patro.
2. Introduction to group theory, Devullpali Vinay Sanyasi.

2024

1. Braid groups, Aarjav Jogani.
2. Free Product and Ping-pong Lemma, Aditya Vikram Saraf.

2023

1. Combinatorial aspects of Coxeter groups, A. Rameswar Patro.

1. Topology (MAT307, M405, MAT803): Int. M.Sc. + Int. M.Sc.-Ph.D., NISER, Fall 2026.
2. Classical Groups (M553, MA880): Int. M.Sc. + Int.M.Sc.-Ph.D., NISER, Spring 2026.
3. Number Theory (M207, M305, MA703): Int. M.Sc. + Int.M.Sc.-Ph.D., NISER, Fall 2025.
4. Field Theory (M307, MA806): Int. M.Sc. + Int.M.Sc.-Ph.D., NISER, Spring 2025.
5. Algebra I (MAT 601): Ph.D., NISER, Fall 2024.
6. Group Theory (M202): Int. M.Sc., NISER, Spring 2024.
7. Topology (M405, MA803): Int. M.Sc. + Int. M.Sc.-Ph.D., NISER, Fall 2023.
8. Metric Spaces (M204): Int. M.Sc., NISER, Spring 2023.
9. Mathematical Analysis (MA702): Int. M.Sc.-Ph.D.,  NISER, Fall 2022.

Conferences/Workshops/Outreach Programs 

1. Automorphisms and Congruence Subgroup Property of Coxeter groups, Workshop on Group Theory 2025, IISER Pune, 17th - 18th November, 2025.
2. Classification of Finite p-groups, Current Progress of Pure & Applied Mathematics in Science and Technology, SCB Baripada, 6th - 7th May, 2025.
3. Breadth type and Classification of Nilpotent Lie algebras, National Seminar on Number Theory and Lie Algebra, Sambalpur University,  27th - 28th February, 2025.
4. Exploring the Dihedral Group $D_{2n}$, Seminar on Group Theory and Distribution of Prime Numbers, Dhenkanal Autonomous College,  15th February, 2025.
5. Delivered a talk on National Mathematics Day, Sundargarh Govt. College, 21st - 23rd December, 2024.
6. Extra-Mural Lecture on Exploring the beauty of Group theory, Sundargarh Govt. College, 19th February, 2024.
7. High-School Algebra, Rural Mathematics Talent Search Program, Dungripali High School, Sonepur, Odisha, December 2023.

Lecture Series:

1. Group Theory: SOPM, NISER, May-June 2024.
2. Combinatorial Group Theory,  Workshop on Group Theory and Around, HRI, December 2023.
3. Number Theory: SOPM, NISER, May-June 2023.

1. Convener, PGCS, SMS, 2024 - till date.
2. Convener, SMS (School of Mathematical Sciences, NISER) Website, (July 2022 - July 2025).
3. Member, Selection Committee for Ph.D. Program, SMS, NISER, 2025
4. Member, Ph.D. Monitoring Committee, SMS, 2023, and 2024.
5. Member, Selection Committee for Int. M.Sc. - Ph.D. Program, SMS, NISER, 2023, and 2024. 
6. Member, Screening Committee for shortlisting Ph.D applications, SMS, NISER, 2024.
7. Member, UGCS, SMS, NISER, 2022 - 2024.