Research and projects

I took a basic approach to Category Theory, mainly referring to Tom Leinster's book on Basic Category theory. I read about categories, functors, natural transformations, adjoint functors, Yoneda Lemma, Yoneda embedding, Limits and Colimits, with particular examples like Product, Coproduct, Pullback, Pushout, Equalizer, etc. Towards the end of the program, I presented what I had been studying, to the audience present at the symposium, held at Sabanci University, Turkey.

This reading project was as a part of the Directed Reading Project (DRP) Turkiye in 2025, mentored by Mr. Mehmet Kirtisoglu for 1.5 months, between July - August 2025.

PFA the presentation here and the report here.

I read about group presentations in terms of generators and relators, free groups, free product and amalgamated product, ping-pong lemma. Apart from this I read about Cayley graphs, building relationship with groups and graphs. 

This project was performed under the supervision of Dr. Tushar Kanta Naik, NISER, Bhubaneswar, India during the period June-August 2024.

PFA my internship report here.

I covered the basics of measure theory, Lebesgue integration, functional analysis during my first internship in the summer of second year of my integrated bs-ms program. By the end I concluded with a view of spectral theory from the book "A short course in Spectral Theory by William Arveson." 

This project was performed under the supervision of Dr. Prahlad Vaidyanathan, IISER Bhopal, India during the period June-July 2023.

PFA my internship report here.