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作者：Popa, Mihnea; schnell, Christian
摘要：We show that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties.
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作者：Zhang, Yitang
摘要：It is proved that lim inf(n ->infinity)(p(n+1)-p(n)) < 7 x 10(7), where p(n) is the n-th prime. Our method is a refinement of the recent work of Goldston, PintzandY1ld1rm on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose.
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作者：Wickramasekera, Neshan
摘要：We give a necessary and sufficient geometric structural condition, which we call the alpha-Structural Hypothesis, for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth hypersurface away from a small set of generally unavoidable sing ularities.The alpha-Structural Hypothesis says that no point of the support of the varifold has a neighborhood in which the support is the union of three or more embedded C-1,C-alpha hypersurfaces-with-boun...
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作者：Zhang, Wei
摘要：By the relative trace formula approach of Jacquet-Rallis, we prove the global Gan-Gross-Prasad conjecture for unitary groups under some local restrictions for the automorphic representations.
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作者：Li, Chi; Xu, Chenyang
摘要：For any flat projective family (X,L) -> C such that the generic fibre X-eta is a klt Q-Fanco variety and L vertical bar(X eta) similar to(Q) -K-X eta , we use the techniques from the minimal model program (MMP) to modify family. The end product is a family such that every fiber is a kit Q-Fanco variety. Moreover, we can prove that the Donaldson-Futski invariants of the appearing models decrease. When the family is a test configuration of a fixed Fanco variety (X,-K-X), this implies Tian's conj...
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作者：Venkataramana, T. N.
摘要：We show that the image of the braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree d. This is deduced by proving the arithmeticity of the image of the braid group on n+1 letters under the Burau representation evaluated at d-th roots of unity when n >= 2d.
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作者：Harvey, David
摘要：Let g >= 1, and let Q is an element of Z[x] be a monic, squarefree polynomial of degree 2g + 1. For an odd prime p not dividing the discriminant of Q, let Z(p)(T) denote the zeta function of the hyperelliptic curve of genus g over the finite field F-p obtained by reducing the coefficients of the equation y(2) = Q(x) modulo p. We present an explicit deterministic algorithm that given as input Q and a positive integer N, computes Z(p)(T) simultaneously for all such primes p < N, whose average co...
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作者：Mj, Mahan
摘要：We prove the existence of Cannon-Thurston maps for simply and doubly degenerate surface Kleinian groups. As a consequence we prove that connected limit sets of finitely generated Kleinian groups are locally connected.
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作者：Kashiwara, Masaki; Vilonen, Kari
摘要：In this paper we give a proof of a fundamental conjecture, the codimension-three conjecture, for microdifferential holonomic systems. The conjecture states that any (regular) holonomic module extends uniquely beyond an analytic subset that is at least of codimension three in its support. Our result can also be interpreted from a topological point of view as a statement about microlocal perverse sheaves. However, our proof is entirely in the context of microdifferential holonomic systems.
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作者：Eberhard, Sean; Green, Ben; Manners, Freddie
摘要：Answering a question of P. Erdos from 1965, we show that for every epsilon > 0 there is a set A of n integers with the following property: every set A' subset of A with at least (1/3 + epsilon) n elements contains three distinct elements x, y, z with x + y = z.
