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. I am no longer interested in these topics, but it would be interesting to see if any of my current work relates to these areas.