Random Cayley Graphs and Expanders
Almost every Cayley graph on c(delta) log n random generators of a group of order n is an expander (Alon-Roichman, 2002)
Improved Batch Code Lower Bounds
A new Omega(sqrt(Nk)) redundancy lower bound for primitive multiset linear batch codes, via the dimension of the dual code's order-O(k) tensor.
Essential Coding Theory
Blueprint of the graduate textbook 'Essential Coding Theory' (Guruswami, Rudra, Sudan) — codes, bounds, constructions, decoding algorithms, and applications.
Expander Codes
Asymptotically good linear codes from expander graphs, with linear-time sequential and logarithmic-depth parallel decoding.
Expander Graphs and Their Applications
Blueprint of the Hoory-Linial-Wigderson survey (Bull. AMS 2006): expansion, eigenvalues, random walks, explicit constructions, codes, and embeddings.
Approximate Gradient Coding with Optimal Decoding
Approximate gradient codes from expander graphs with optimal decoding coefficients, and convergence bounds for random and adversarial stragglers.
When Do Low-Rate Concatenated Codes Approach the Gilbert-Varshamov Bound?
Sufficient conditions on an outer code so that concatenation with a single random linear inner code lies on the GV bound.
Magic and Communication Complexity
Low-magic quantum circuits have low communication cost: magic lower bounds from communication, and exponential R-parallel separations.
Efficient Near-Optimal Codes for General Repeat Channels
Explicit capacity-approaching codes for all square-integrable D-repeat channels, encodable and decodable in linear / quasi-linear time.
Spectral Graph Theory
Blueprint of Fan Chung's monograph (CBMS no. 92, 1996): the normalized Laplacian, eigenvalues, Cheeger constants, diameters, routing, quasi-randomness, expanders, boundary conditions, Harnack inequalities, heat kernels, and Sobolev inequalities.
Fundamental Limitations on Subquadratic Alternatives to Transformers
Under fine-grained complexity assumptions, document-similarity tasks transformers can solve cannot be solved in truly subquadratic time.