Keshab Chandra Bakshi

Welcome to my academic homepage. I am an Associate Professor (since July 2025) in the Department of Mathematics at the Indian Institute of Technology (IIT) Kanpur, where I previously served as an Assistant Professor from 25th April 2022 to 30th June 2025.

My research centers on operator algebras---specifically Vaughan Jones' subfactor theory, planar algebras, Connes–Størmer relative entropy, quantum symmetries, and finite-index inclusions of C*- and von Neumann algebras. A central theme of my research is understanding how the relative position of subalgebras influences their structure, symmetries, and invariants, including index, depth, angles, and quantum relative entropy. My research group is supported by the Prime Minister Early Career Research Grant (ANRF), Government of India.

Previously, I held a DST-INSPIRE Faculty Fellowship (2020–2022) and an NBHM Postdoctoral Fellowship (2018–2020) at the Chennai Mathematical Institute (CMI). I earned my Ph.D. in Mathematics from The Institute of Mathematical Sciences (IMSc, HBNI), Chennai in 2018 under the supervision of Prof. V. S. Sunder, following my M.Sc. at TIFR CAM Bangalore and B.Sc. (Hons.) at Ramakrishna Mission Vidyamandira, Belur Math (University of Calcutta).

Prospective Ph.D. students and postdoctoral fellows interested in subfactor theory, C*-inclusions, or quantum symmetries are welcome to write to me at keshab@iitk.ac.in.

Office Address (Office 558, Department of Mathematics, IIT Kanpur) and Emails (keshab@iitk.ac.in, bakshi209@gmail.com) .

The symmetries of an operator algebra are often revealed through its subalgebras, their relative positions, and the towers of relative commutants they generate. (Inspired by the work of Vaughan Jones, founder of subfactor theory)

Work in progress:

(a) Two Subfactors and Quantum Relative Entropy, in preparation.

(b) A note on Pimsner-Popa bases, joint with Rajarama Bhat , forthcoming.

Selected Publications

An angle between intermediate subfactors and its rigidity, with S. Das, Z. Liu and Y. Ren; Transactions of the American Mathematical Society (2019).
Lattice of intermediate subalgebras, with V. Gupta; Journal of the London Mathematical Society (2021).
Commuting squares and planar subalgebras, with V. Kodiyalam; Journal of Opeartor Theory (2021).
Unitary orthonormal bases of finite dimensional inclusions, with. BVR Bhat; International Mathematics Research Notices (2025).
A family of subfactors arising from a pair of complex Hadamard matrices, with S. Guin; International Journal of Mathematics (2025).
Weak quantum hypergroups from finite-index C-inclusions, with D. Goswami and B. Pal; International Mathematics Research Notices (2026).

For the complete list, see Publications and Preprints.

Research Collaborators

Rajarama Bhat, Sayan Das, Indrajit Ghosh, Debashish Goswami, Ved Prakash Gupta, Satyajit Guin, Guruprasad, Debabrata Jana, Vijay Kodiyalam, Sumit Kumar, Zhengwei Liu, Biplab Pal, Yunxiang Ren, Silambarasan C., Sruthymurali...