In a recent breakthrough, Williams (STOC 2025) showed that any decision problem solvable in time $t$ by a multitape Turing machine can be solved in space $\tilde{O}(\sqrt{t})$ and time $2^{\tilde{O}(\sqrt{t})}$. The immediate question is whether this result is an anomaly, or an inherent feature of computation more generally.

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Understanding the limits of list-decodability of Reed-Solomon codes has been one of the most important open problems in algebraic coding theory. Recently, Brakensiek, Chen, Putterman, Zhang, and Zheng, in a remarkable breakthrough, showed that Reed-Solomon (RS) codes over fields of large characteristic are algorithmically list-decodable all the way up to ... more >>>

We study the query complexity of finding a Tarski fixed point over $[n]^k$. Previous work has left a large gap between $\smash{{\Omega}(\log^2 n)}$ and $\smash{\log^{O(k)}n}$. We show that both of the previous upper and lower bounds were far from tight: for every $k\geq 3$,
$$
\Omega\left((\log n)^{\frac{1}{2}\lceil \log k\rceil}\right)\le
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