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作者：Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
摘要：The classical Birkhoff conjecture claims, that the boundary of strictly convox integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we show that a version of this conjecture is true for tables bounded by small perturbations of ellipses of small eccentricity.
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作者：Maynard, James
摘要：We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1 + o(1))(logx)(log log x) (log log log log x) (log log log x)(-2) for any fixed t. This answers a well-known question of Erdos.
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作者：Jannsen, Uwe
摘要：For rather general excellent schemes X, K. Kato defined complexes of Gersten-Bloch-Ogus type involving the Galois cohomology groups of all residue fields of X. For arithmetically interesting schemes, he developed a fascinating web of conjectures on some of these complexes, which generalize the classical Hasse principle for Brauer groups over global fields, and proved these conjectures for low dimensions. We prove Kato's conjecture over number fields in any dimension. This gives a cohomological...
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作者：Kaletha, Tasho
摘要：We define a new cohomology set H-1(u -> W, Z -> G) for an affine algebraic group G and a finite central subgroup Z, both defined over a local field of characteristic zero, which is an enlargement of the usual first Galois cohomology set of G. We show how this set can be used to give a precise conjectural description of the internal structure and endoscopic transfer of tempered L-packets for arbitrary connected reductive groups that extends the well-known conjectural description for quasi-split...
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作者：Miller, Jason; Sheffield, Scott
摘要：Suppose that D subset of C is a Jordan domain and x, y is an element of partial derivative D are distinct. Fix k is an element of (4, 8), and let eta be an SLEk process from x to y in D. We prove that the law of the time-reversal of eta is, up to reparametrization, an SLEk, process from y to x in D. More generally, we prove that SLEk(rho(1); rho(2)) processes are reversible if and only if both rho(i), are at least k/2 - 4, which is the critical threshold at or below which such curves are bound...
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作者：Linial, Nathan; Peled, Yuval
摘要：It is well known that the G(n,p) model of random graphs undergoes a dramatic change around p = 1/n It is here that the random graph, almost surely, contains cycles, and here it first acquires a giant (i.e., order Omega(n)) connected component. Several years ago, Linial and Meshulam introduced the Y-d(n,p) model, a probability space of n-vertex d-dimensional simplicial complexes, where Y-1(n,p) coincides with G(n,p). Within this model we prove a natural d-dimensional analog of these graph theor...
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作者：Malle, Gunter; Spaeth, Britta
摘要：We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes such that a Sylow l-subgroup or its maximal normal abelian subgroup is contained in a maximally split torus by means of a new equivariant version of Harish-Chandra induction. Specifics of characters of odd degree, namely, that most of them lie in the principal Harish-Chandra series, then allow us to deduce from it the McKay ...
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作者：Dafermos, Mihalis; Rodnianski, Igor; Shlapentokh-Rothman, Yakov
摘要：This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior space times I-II: the cases vertical bar a vertical bar << M or axisymmetry, arXiv:1010.5132], providing the complete proof of definitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal vertical bar a vertical bar < M case without symmetry assumptions. The essential ideas of the proof (together with explicit...
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作者：Matomaki, Kaisa; Radziwill, Maksym
摘要：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 Mobius function we show that there are cancellations in the sum of mu(n) in almost all intervals of the form [x, x + psi(x)] with psi(x) -> infinity arbitrarily slowly. This goes beyond what was previously known conditionally on the Density Hypothesis or the stronger Riemann Hypothesis. Second, we settle the long-sta...
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作者：Kapranov, Mikhail; Schechtman, Vadim
摘要：Let H be an arrangement of real hyperplanes in R. The complexification of H defines a natural stratification of C. We denote by Perv(C-n,H) the category of perverse sheaves on C-n smooth with respect to this stratification. We give a description of Perv(C-n,H)as the category of representations of an explicit quiver with relations, whose vertices correspond to real faces of H (of all dimensions). The relations are of monomial nature: they identify some pairs of paths in the quiver. They can be ...
