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作者：Dittmann, Philip; Pop, Florian
摘要：We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class, there is a first-order sentence that characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.
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作者：Rodnianski, Igor; Shlapentokh-Rothman, Yakov
摘要：In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in 3 + 1 dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation.Prior to this work, the only known examples of naked singularities wer...
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作者：Conde-Alonso, Jose M.; Gonzalez-Perez, Adrian M.; Parcet, Javier; Tablate, Eduardo
摘要：We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers S-M on Schatten p-classes which solves a conjecture proposed by Mikael de la Salle. Given 1 < p < infinity, a simple form of our main result for R-n x R-n matrices reads as follows: ||S-M : S-p -> S-p||(cb) less than or similar to p(2)/p-1 Sigma(|gamma|less than or similar to[n/2]+1)|||x y|(|gamma|) {|partial derivative M-gamma(x)(x, y) | + |partial derivative M-gamma(y)(x , y)|}||(proportional to). ...
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作者：Schumacher, Georg; Tsuji, Hajime
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作者：Guo, Bin; Phong, Duong H.; Tong, Freid
摘要：A PDE proof is provided for the sharp L & INFIN; estimates for the complex Monge-Ampe`re equation that had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.
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作者：Aggarwal, Amol
摘要：In this paper we consider uniformly random lozenge tilings of arbitrary domains approximating (after suitable normalization) a closed, simply-connected subset of R-2 with piecewise smooth, simple boundary. We show that the local statistics of this model around any point in the liquid region of its limit shape are given by the infinite-volume, translation-invariant, extremal Gibbs measure of the appropriate slope, thereby confirming a prediction of Cohn-Kenyon-Propp from 2001 in the case of loz...
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作者：D'Addezio, Marco
摘要：In this article we prove Crew's parabolicity conjecture of F-iso crystals. For this purpose, we introduce and study the notion of & DAG;-hull of a sub-F-iso-crystal. On the way, we prove a new Lefschetz theorem for overconvergent F-iso crystals.
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作者：Yu, Hongjie
摘要：Let X1 be a projective, smooth and geometrically connected curve over Fq with q = p' elements where p is a prime number, and let X be its base change to an algebraic closure of Fq. We give a formula for the number of irreducible B-adic local systems (B =6 p) with a fixed rank over X fixed by the Frobenius endomorphism. We prove that this number behaves like a Lefschetz fixed point formula for a variety over Fq, which generalises a result of Drinfeld in rank 2 and proves a conjecture of Deligne...
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作者：Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio
摘要：We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted by Spohn; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity a...
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作者：Moeller, Sven; Scheithauer, Nils R.
摘要：We prove a dimension formula for the weight-1 subspace of a vertex operator algebra Vorb(g) obtained by orbifolding a strongly rational, holo-morphic vertex operator algebra V of central charge 24 with a finite-order automorphism g. Based on an upper bound derived from this formula we introduce the notion of a generalised deep hole in Aut(V ).Then we show that the orbifold construction defines a bijection between the generalised deep holes of the Leech lattice vertex operator algebra V Lambda ...
