We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for $A \subseteq \mathbb{F}_2^n$ with doubling constant $K$, learn an explicit description of a subspace $V \subseteq \mathbb{F}_2^n$ ... more >>>

We consider the query complexity of testing whether a bounded-degree graph is expanding, regardless of whether or not it is connected.

Whereas prior work studied testing the property of being an expander (equiv., testing the set of expander graphs), here we study testing the set of graphs that consist of ... more >>>

We first extend the results of CKSV22 by showing that the degree $d$ elementary symmetric polynomials in $n$ variables have formula lower bounds of $\Omega(d(n-d))$ over fields of positive characteristic.
Then, we show that the results of the universality of the symmetric model from Shp02 and the results about border ... more >>>