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作者：Harris, Michael; Shepherd-Barron, Nick; Taylor, Richard
摘要：We prove potential modularity theorems for l-adic representations of any dimension. From these results we deduce the Sato-Tate conjecture for all elliptic curves with nonintegral j-invariant defined over a totally real field.
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作者：Saito, Shuji; Sato, Kanetomo; Jannsen, Uwe
摘要：Let R be a henselian discrete valuation ring. Let X be a regular projective flat scheme over Spec (R) with generalized semistable reduction. We prove a bijectivity theorem for etale cycle class maps of the Chow group of 1-cycles on X. As an application, we prove a finiteness theorem for the Chow group of 0-cycles on a projective smooth variety over a p-adic field.
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作者：Chatterjee, Sourav; Peled, Ron; Peres, Yuval; Romik, Dan
摘要：For d >= 3, we construct a non-randomized, fair, and translation-equivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R-d, defined by allocating to each of the Poisson points its basin of attraction with respect to the flow induced by a gravitational force field exerted by the points of the Poisson process. We prove that this allocation rule is economical in the sense that the allocation diameter, defined as the diameter X of the basin of attraction c...
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作者：Akbulut, Selman
摘要：We show here that an infinite sequence of homotopy 4-spheres constructed by Cappell-Shaneson are all diffeomorphic to S-4. This generalizes previous results of Akbulut-Kirby and Gompf.
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作者：Holowinsky, Roman; Soundararajan, Kannan
摘要：We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors.
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作者：Burger, Marc; Iozzi, Alessandra; Wienhard, Anna
摘要：We develop the theory of maximal representations of the fundamental group pi(1) (Sigma) of a compact connected oriented surface Sigma ( possibly with boundary) into Lie groups G of Hermitian type. For any homomorphism rho : pi(1)(Sigma) -> G, we define the Toledo invariant T (Sigma, rho), a numerical invariant which has both topological and analytical interpretations. We establish important properties of T T (Sigma, rho), among which continuity, uniform boundedness on the representation variet...
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作者：Lindblad, Hans; Rodnianski, Igor
摘要：We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach, which relies on the classical harmonic gauge, shows that the Einstein-vacuum and the Einstein-scalar field equations with asymptotically flat initial data satisfying a global smallness condition produce global (causally geodesically complete) solutions asymptotically convergent to the Minkowski space-time.
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作者：Balazs, Marton; Seppalainen, Timo
摘要：We prove that the variance of the current across a characteristic is of order t(2/3) in a stationary asymmetric simple exclusion process, and that the diffusivity has order t(1/3). The proof proceeds via couplings to show the corresponding moment bounds for a second class particle.
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作者：Bringmann, Kathrin; Ono, Ken
摘要：Motivated by work of Ramanujan, Freeman Dyson defined the rank of an integer partition to be its largest part minus its number of parts. If N(m, n) denotes the number of partitions of n with rank m, then it turns out that R(w; q) : = 1 + Sigma(infinity)(n=1) Sigma(infinity)(m=-infinity) N(m, n)w(m)q(n) = 1 + Sigma(infinity)(n=1) q(n2)/Pi(n)(j=1)(1-(w+w(-1))q(j) + q(2j)). We show that if zeta not equal 1 is a root of unity, then R(zeta; q) is essentially the holomorphic part of a weight 1/2 wea...
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作者：Lewis, John; Nystrom, Kaj
摘要：In a previous article, we proved a boundary Harnack inequality for the ratio of two positive p harmonic functions, vanishing on a portion of the boundary of a Lipschitz domain. In the current paper we continue our study by showing that this ratio is Holder continuous up to the boundary. We also consider the Martin boundary of certain domains and the corresponding question of when a minimal positive p harmonic function (with respect to a given boundary point w) is unique up to constant multiple...
