• Leavitt path algebras and their generalisations
• Steinberg algebras and Groupoid C* algebras
• Non-commutative Stone duality and Boolean inverse semigroups
• Semigroup Theory

Mohan completed his doctoral degree from Indian Statistical Institute, Bangalore Centre. He has earlier taught in Amrita Vishwa Vidyapeetham’s Bengaluru campus and was a field associate at Azim Premji Foundation’s Puducherry District Institute.

His doctoral work was on Cohn-Leavitt path algebras of bi-separated graphs, which builds a common framework for Leavitt path algebras and their various generalisations. He also studied their non-stable K‑theory and representation theory in a few special cases.

In recent years, étale groupoids have become a focal point in several areas of mathematics. The convolution algebras arising from étale groupoids, considered both in analytical setting (groupoid C* algebras pioneered by Renault) and algebraic setting (Steinberg algebras). They include many deep and important examples such as graph C* algebras and Leavitt path algebras, and allow systematic treatment of them. 

On the other hand, partial symmetries arising in dynamical systems can be realised by étale groupoids via inverse semigroups. This has led to a fertile confluence of different areas of mathematics such as non-commutative algebras, inverse semigroup theory, and C* algebras. His research interests are focused on the study of how these areas interact with each other. He is also interested in undergraduate mathematics education and communication. 

He is the multi-media editor at Bhavana, the mathematics magazine, and runs Math Nomad, a YouTube channel. He enjoys long walks, and listening to music, audiobooks and podcasts.