Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture...
We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let $\ell > 2$ be...
View ArticleDecay for solutions of the wave equation on Kerr exterior spacetimes III: The...
This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: the cases $|a| \ll M$ or axisymmetry,...
View ArticleLarge gaps between primes
We show that there exist pairs of consecutive primes less than $x$ whose difference is larger than \[ t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}\] for any fixed $t$....
View ArticleLarge gaps between consecutive prime numbers
Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdős, we show that \[ G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log...
View ArticleClassicité de formes modulaires surconvergentes
Nous généralisons le critère de classicité de formes modulaires surconvergentes sur les courbes modulaires dû à Coleman à certaines variétés de Shimura PEL de type (A) et~(C) associées à des groupes...
View ArticleMultiplicative functions in short intervals
We introduce a general result relating “short averages” of a multiplicative function to “long averages” which are well understood. This result has several consequences. First, for the Möbius function...
View ArticleErrata of “Isoparametric hypersurfaces with $(g,m)=(6,2)$”
We give a correction of the proof of the homogeneity of isoparametric hypersurfaces with $(g,m)=(6,2)$.
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