Research Interests

My broad interests are in Computational Complexity Theory. I am interested in studying about the various resources utilized in Computation, and problems that arise therein. In these, I am particularly interested in Algebraic and Geometric Complexity Theory, Pseudorandomness and Coding Theory

Algebraic and Geometric Complexity Theory

My current work broadly revolves in these areas, where I am trying to study the classical problem of Polynomial Identity Testing over non-commutative rings. The commutative case has been well studied, but for the non-commutative case, even a randomized algorithm for polynomials with very high sparsity seems elusive. However, recent work in lower bounds gives us some hope.

Pseudorandomness

Apart from these, I love studying about randomness in computation. Whether randomness is essential for computation is a core problem in computer science. This is also a natural question, since even for humans, time and resources always seem to be scarce.

I am trying to learn more about pseudorandomness, particularly about expanders and pseudorandom generators. I find derandomization absolutely magical, and is one of the core motivations for my research. I find the Hardness vs. Randomness paradigm very interesting, especially the recent work towards resolving BPP vs P conjecture.

I am also trying to understand a bit more about space bounded derandomization as well, and work towards resolving BPL vs L, which seems to be rather close :)

Error Correcting Codes

I am interested in problems in coding theory that use techniques from algebra and pseudorandomness.

My ultimate aim would be to marry a few of these ideas together. (Sorry for the pun, but I could not resist. )

If you have a problem you think I might find interesting, hit me up :)

In the past I have worked in Dimensionality Reduction for Deep Learning and Isogeny based Techniques for Post Quantum Cryptography.It would be interesting to see if any of my current work relates to these areas!