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Article
Open AccessMonotone Nondecreasing Sequences of the Euler Totient Function
Let M(x) denote the largest cardinality of a subset of \(\{n \in \mathbb {N}: n \le x\}\) ...
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Article
Open AccessPerfectly Packing a Square by Squares of Nearly Harmonic Sidelength
A well-known open problem of Meir and Moser asks if the squares of sidelength 1/n for \(n\ge 2\) ...
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Article
Open AccessUndecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile
We construct an example of a group \(G = \mathbb {Z}^2 \times G_0\) G ...
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Article
Open AccessLarge prime gaps and probabilistic models
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigor...
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Correction to: Fourier uniformity of bounded multiplicative functions in short intervals on average
The original version of this article unfortunately contains a mistake.
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Article
Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation
In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as ...
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Article
Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations
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The asymptotic distribution of a single eigenvalue gap of a Wigner matrix
We show that the distribution of (a suitable rescaling of) a single eigenvalue gap \(\lambda _{i+1}(M_n)-\lambda _i(M_n)\) of a...
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On Sets Defining Few Ordinary Lines
Let \(P\) P be ...
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Erratum to “The primes contain arbitrarily long polynomial progressions”
In our previous paper “The primes contain arbitrarily long polynomial progressions” [Acta Math., 201 (2008), 213–305] there were some minor errors in our definition of the polynomial forms and polynomial correlat...
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Outliers in the spectrum of iid matrices with bounded rank perturbations
It is known that if one perturbs a large iid random matrix by a bounded rank error, then the majority of the eigenvalues will remain distributed according to the circular law. However, the bounded rank perturb...
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An Incidence Theorem in Higher Dimensions
We prove almost tight bounds on the number of incidences between points and k-dimensional varieties of bounded degree in R d . Our main tools are the polynomial ...
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Open AccessA Finitary Version of Gromov’s Polynomial Growth Theorem
We show that for some absolute (explicit) constant C, the following holds for every finitely generated group G, and all d > 0: If there is some R 0 > exp(exp(Cd ...
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Article
Open AccessRandom Matrices: Universality of Local Eigenvalue Statistics up to the Edge
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/0908.1982v4[math.PR], 2010) on the universality of the eigenvalues of Wigner ra...
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Open AccessAn Inverse Theorem for the Uniformity Seminorms Associated with the Action of \({{\mathbb {F}^{\infty}_{p}}}\)
Let \({\mathbb {F}}\) a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra unifor...
