Tushar Kanta Naik

Designation

Assistant Professor

Joining Date

29/06/2022

Research Area

Algebra

Education

Research Interest

Finite group theory: Classification of p-groups, the influence of conjugacy class sizes on the structure of finite groups, Automorphisms of finite groups, Word maps, and Various graphs associated with finite groups.
Combinatorial group theory: Coxeter groups and Artin groups, specific interest in the isomorphism problem of Coxeter groups.
Groups in low dimensional topology: Braid groups, Planar braid groups (twin groups / traid groups (physics)), their virtual analogous and pure subgroups.
(Nilpotent) Lie algebra: Classification of finite dimensional nilpotent Lie algebras, Camina Lie algebras, Breadth of a Lie algebra.

Awards

Publications

( _, and Mahender Singh), Automorphisms of odd Coxeter groups, Monatsh. Math., 195 (3), 2021, 501 – 521.
(_, Neha Nanda, and Mahender Singh), Some remarks on twin groups, J. Knot Theory Ramifications, 29 (10), 2020, 2042006, 14 pp.
(_, Neha Nanda, and Mahender Singh), Conjugacy classes and automorphisms of twin groups, Forum Math., 32 (5), 2020, 1095 – 1108.
(_, 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.
_, On the probability distribution associated to commutator word map in finite groups, Communications in Algebra, 47 (9), 2019, 3808 – 3817.
(_, and Manoj K. Yadav), Finite p-groups of conjugate type {1, p³}, J. Group Theory, 21 (1), 2018, 65 – 82.

Preprints

(Pravin Kumar, _, and Mahender Singh), Congruence subgroups and crystallographic quotients of small Coxeter groups, 22pp., arXiv:2212.09084.
(Rijubrata Kundu, _, and Anupam Singh), Nilpotent Lie algebras with two centralizer dimensions over a finite field, 25pp., arXiv:2208.07676.
(Rijubrata Kundu, _, and Anupam Singh), Nilpotent Lie algebras of breadth type (0, 3), 24pp., arXiv:2111.04968.
(_, Neha Nanda, and Mahender Singh), Virtual twin groups and permutations, 30pp., arXiv:2109.13035.
(_, Neha Nanda, and Mahender Singh), Structural aspects of pure virtual twin groups, 31pp, arXiv:2008.10035.

Teaching

Responsibility

Academic Presentations

Breadth type of (nilpotent) Lie algebras”, (online) Workshop on Group Theory 2022, 04th February, 2022, https://sites.google.com/site/anupamk182/wgt22?authuser=0.
“Automorphisms of three canonical extensions of symmetric groups,”, World of GroupCraft 2021 (World of geometric group theory - online international conference), 26th August, 2021.
“Automorphisms of (odd) Coxeter groups (A study motivated by Artin braid groups and twin groups)”, Group Theory Sangam (online conference), 03rd June, 2021.
“Finite groups with exactly two conjugacy class sizes and the analogous study in Lie algebra”, weekly online seminar @ Gonit Sora, 19th March, 2021.
“Finite groups with two conjugacy class sizes”, Workshop on Group Theory 2020, IISER Pune, India, 13th February, 2020.
“Twin and Pure twin groups”, Harish-Chandra Research Institute, Prayagraj (Allahabad), In- dia, 06th February, 2020.
“Twin groups”, Young Mathematicians Symposium, IISER Mohali, India, 07th December, 2019.
“On p-groups of conjugate type (1, p3)”, 83rd Annual conference of Indian Mathematical Society, SV University, Tirupati, India, 13th December, 2017.
“On p-groups of conjugate rank 1 and nilpotency class 3”, Groups St Andrews 2017, Birmingham, UK, 12th August, 2017.

Academic Visits

NISER Bhubaneswar, India, 10th May - 12th May, 2022.
HRI Prayagraj, India, 22nd July - 28th July, 2019 and 03rd February - 09th February, 2020.
IISER Pune, India, 21st February - 03rd March, 2019 and 09th February - 16th February, 2020.

Events :: Conference/Workshop/Talks link

Useful links