Border complexity captures polynomials that can be approximated arbitrarily well by small algebraic circuits, and debordering asks how efficiently such an approximation can be converted into an exact computation. Debordering lies at the heart of the gap between Valiant's determinant versus permanent conjecture and its strengthening by Mulmuley and Sohoni ... more >>>

We prove an $\Omega((\log n/\log\log n)^2)$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions. This improves the $\widetilde{\Omega}(\log^{3/2} n)$ lower bound of Larsen and Yu [SICOMP 2025], and matches the ... more >>>

In a recent breakthrough, Chattopadhyay, Hatami, Lee, Lovett, Tal, and Viola (ECCC'26) established exponential correlation bounds for polynomials over $\mathbf{F}_2$ and, as a consequence, obtained a major improvement in PRG constructions for low-degree polynomials over the binary field. In particular, they obtained seed length $\widetilde{O}(d^2\log^2 n)$ for fooling degree-$d$ polynomials ... more >>>