Certificate complexity $(C(f ))$ is a fundamental measure of complexity of Boolean functions $f$
which counts the number of bits of an input that need to be known in order for the value of the
function to be determined. A certificate can be viewed as a partial assignment, or a ... more >>>

The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free families of subsets of a fixed ground set. We show that for $k\ge4$, every tensor that is nonzero exactly on the $k$-term arithmetic progression relation or ... more >>>

We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas (2026) about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick (2024) for constructing quantum LTCs, instantiated with ... more >>>