Claims a proof of the paraboloid Fourier extension conjecture in d≥3 via smooth Alpert wavelets, grid averaging, and a periodic stationary phase lemma.
arXiv preprint arXiv:2502.17655 , year=
6 Pith papers cite this work. Polarity classification is still indexing.
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The authors prove that the Fourier dimension Δ(s,t) of any (s,t)-Kakeya set in the plane satisfies 2st/(s+2t) ≤ Δ(s,t) ≤ min{s,2t} for 0<s,t<1, with analogous bounds in the Furstenberg and Fourier-direction variants.
Derives exact values and asymptotic bounds on the maximum and minimum densities of k-in-a-row avoiding configurations on Z^2 and [k]^d.
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
A survey sketching the proof of the three-dimensional Kakeya conjecture by Wang and Zahl.
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A smooth Alpert testing characterization of convolution type for the Fourier extension conjecture on paraboloids
Claims a proof of the paraboloid Fourier extension conjecture in d≥3 via smooth Alpert wavelets, grid averaging, and a periodic stationary phase lemma.
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Fourier analytic variants of the Furstenberg and Kakeya problems
The authors prove that the Fourier dimension Δ(s,t) of any (s,t)-Kakeya set in the plane satisfies 2st/(s+2t) ≤ Δ(s,t) ≤ min{s,2t} for 0<s,t<1, with analogous bounds in the Furstenberg and Fourier-direction variants.
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Monochromatic $k$ in a row
Derives exact values and asymptotic bounds on the maximum and minimum densities of k-in-a-row avoiding configurations on Z^2 and [k]^d.
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Mathematical exploration and discovery at scale
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
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The Kakeya conjecture, after Wang and Zahl
A survey sketching the proof of the three-dimensional Kakeya conjecture by Wang and Zahl.
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