Operator algebra and functional analysis:

(1) C* - algebras and von Neumann algebras.

(1) Subfactors and planar algebras.

(2) Completely positive maps, C*- convexity (quantum convexity).

(3) Semigroup C*- algebras, Dynamical systems, analysis of KMS(Kubo- Martin- Schwinger) states.

PhD: IMSc Chennai, 2021

Postdoctoral Experiences:

1. CMI, Chennai - August 2020- October 2022.
2. ISI, Bangalore - November 2022- June 2023

(1) On a presentation of the spin planar algebra, (Jointly with Vijay Kodiyalam, Sohan Lal Saini, and V S Sunder), Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 2, Art. 27, 11 pp.

(2) Planar algebras, quantum information theory and subfactors, (Jointly with Vijay Kodiyalam and V S Sunder), Internat. J. Math. 31 (2020), no. 14, 2050124, 21pp.

(3) Planar algebras associated to Latin squares are of subgroup-group type, (Jointly with Vijay Kodiyalam), Proc. Amer. Math. Soc. 149 (2021), no. 1, 163–172.

(4) Intermediate planar algebras, revisited II, (Jointly with Keshab Chandra Bakshi), Internat. J. Math. 33(2022), no. 05, 2250033, 12pp.

(5) KMS states on $C_c^*(\mathbb{N}^2)$}, (Jointly with Anbu Arjunan and S Sundar), Glasg. Math. J., https://doi.org/10.1017/S0017089523000071, published online(2023).

(6) Fourier theoretic inequalities for inclusion of simple $C^*$ -algebras, (Jointly with Keshab Chandra Bakshi and Satyajit Guin), New York J. Math., 29(2023), 335-362.

(7) Understanding Quantum Instruments Through the Analysis of C-Convexity and Their Marginals* (with B. V. Rajarama Bhat and Arghya Chongdar). arXiv:2509.11785, 2025. Accepted for publication in Journal of Mathematical Physics.

(8) Higher reflections and entropy of canonical shifts for inclusions of $C^*$ - algebras with finite Watatani index (with Keshab Chandra Bakshi, Biplab Pal and Satyajit Guin). International Journal of Mathematics, Vol. 37, No. 01, 2650007 (2026).

(9) Noncommutative BKW-operators (with C. S. Arunkumar). Positivity, Vol. 29, Article 62 (2025).