What this is? Why am I doing it?

As is usual for a grad student, I read a bunch of articles, books etc. I've found that my understanding is greatly enhanced in the process of writing down an exposition/summary. I've thus decided to write-up these for important papers irrespective of whether I give a talk on these. I also hope that this would improve my writing skills which are terrible at best. If you ever do read any of these, I would love to hear about any errors/comments/suggestions you may have.

HDX — Notes on Trickle-Down and Random Walks

Notes on a pair of lectures by Tali Kaufman as part of the 2022 Summer School on New tools for optimal mixing of Markov chains: Spectral independence and entropy decay.
Thanks - To Eric and Daniel for proofreading and improving the presentation.

Quantum LDPC Codes: An exposition of recent results

An exposition of tensor-product based constructions starting from the hypergraph product of Tillich and Zémor and leading up to the recent breakthrough construction of Pantaleev and Kalachev'21. Also my Master's thesis!
Note - This is a working draft and an expositon of PK21 needs to be added.

Introduction and a Survey

Introduction to the area of computational invariant theory, its connections to computational complexity and a brief survey of recent results

Construction of one-sided high-dimensional expanders (HDX)

An exposition of the paper by Kaufman and Oppenheim as part of the reading group on high-dimensional expanders. There's also a simplified proof by Prahladh Harsha and Ramprasad Saptharishi.

Non-Commutative Rank

Exposition of a set of 2 papers by Ivanyos, Qiao and Subrahmanyam which give a polynomial time-deterministic algorithm to compute non-commutative rank.

Vanishing Kronecker Coefficient

Exposition of (a part of) a recent paper by Ikenmeyer, Mulmuley and Walter on the NP-hardness of computing the vanishing of a Kroncker coefficient.

Milnor-Thom bound

Handout of a talk given as part of the GCT course regarding the Milnor-Thom bound on the number of connected components.