We introduce a variant of a polynomial family called $\TQBFfamily$ obtained from `arithmetization' of the popular $\PSPACE$-complete problem - $\TQBF$. This polynomial family has several nice characteristics such as: $\TQBFfamily \in \VPSPACE_b$, where $\VPSPACEb$ is the `bounded' algebraic version of $\PSPACE$, it is \emph{self-testable}, it captures the computational power of ... more >>>

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 >>>