A method to find the volume of a sphere in the Lee metric, and its applications - Based on the paper of the same name, where we use generating functions and Sanov’s theorem from large deviations theory to find bounds on the sizes of balls in discrete metrics, especially the Lee metric. Given at ISIT 2019. [slides]

Shared Randomness in AVCs - Based on the paper Shared Randomness in Arbitrarily Varying Channels, where we extended previously known results to obtain a precise threshold on the amount of common randomness that is necessary and sufficient to communicate reliably in the presence of an adversary over a state-deterministic AVC and an omniscient adversary. Given at ISIT 2019. [slides]

Two Representations of Graphs Compared - Comparison of Alon’s polynomial based method and Lovasz’s linear algebraic technique of graph representations and how the various basic lemmas and theorems in the two relevant papers are analogous in many ways. Also a discussion of Alon’s counterexample to Shannon’s conjecture on additivity of graph capacities. Given as a part of a course on Techniques in Combinatorics. [notes]

The Lovasz Theta function, a pentagon and an umbrella - An introduction to zero-error information theory and the problem of finding the Shannon capacity of the pentagon, and how it was resolved by Lovasz and his theta function. Presented at Science Coffeehouse, IIT Kanpur [notes]

Approximate Degree of Polynomials and Quantum Query Complexity - Survey talk regarding approximate of polynomials, it’s relationship with quantum query complexity and an explicit construction of an approximating polynomial for the OR function. [slides]

Quantum Information Theory - Introductory talk on the resource theory of quantum information, given as a part of a Quantum Computing course. [slides]

Noisy quantum systems - Introductory talk on density matrices and how they allow us to handle ‘real-life’ quantum mechanics where no state is pure. Also introduces quantum channels. Given as a part of a Quantum Computing course. [slides]

Evolutionary dynamics of language - Survey talk on the Nowak-Niyogi-Komarova model of language evolution, including an overview of the model, known results and possible extensions. Given as part of a Psychology of Language course. [slides]