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arXiv:2606. 17000v1 Announce Type: cross Abstract: We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials.
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
arXiv:2609.08736v1 Announce Type: new Abstract: We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomat...
arXiv:2606. 06136v1 Announce Type: cross Abstract: We prove the positive-real $n=9$ case of the Vasc cyclic inequality.
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
arXiv:2606. 03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$.