Swastik Kopparty

Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers

We extend the “method of multiplicities” to get the following results, of interest in combinatorics and randomness extraction. (i) We show that every Kakeya set in

High-rate codes with sublinear-time decoding

\mathbb{F}_q^n

How to Construct a Correct and Scalable iBGP Configuration

, the

Affine dispersers from subspace polynomials

n

On the list-decodability of random linear codes

-dimensional vector space over the finite field on

Tolerant Linearity Testing and Locally Testable Codes

q

Affine Dispersers from Subspace Polynomials

elements, must be of size at least

Explicit Subspace Designs

q^n/2^n

High-rate locally-correctable and locally-testable codes with sub-polynomial query complexity

. This bound is tight to within a

Equivalence of Polynomial Identity Testing and Deterministic Multivariate Polynomial Factorization

2+o(1)