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作者：Varju, Peter Pal
摘要：Fix a probability measure on the space of isometrics of Euclidean space R-d. Let Y-0 = 0, Y-1, Y-2,... is an element of R-d be a sequence of random points such that Yl+1 is the image of Yi under a random isomrnetry of the previously fixed probability law, which is independent of Y-l. We prove a Local Limit Theoremrn for Y-l under necessary nondcgeneracy conditions. Moreover, under more restrictive but still general conditions we give a quantitative estimate which describes the behavior of the ...
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作者：Scholze, Peter
摘要：The main result of this paper is the existence of Galois representations associated with the mod p (or mod p(m)) cohomology of the locally symmetric spaces for GL(n) over a totally real or CM field, proving conjectures of Ash and others. Following an old suggestion of Clozel, recently realized by Harris-Lan-Taylor-Thorne for characteristic 0 cohomology classes, one realizes the cohomology of the locally symmetric spaces for GL(n) as a boundary contribution of the cohomology of symplectic or un...
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作者：Lackenby, Marc
摘要：We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)(11) Reidemeister moves.
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作者：Colding, Tobias H.; Minicozzi, William P., II
摘要：This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for nonsimply connected embedded minimal surfaces of any given fixed genus. The first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely-oriented double spiral staircases. The second gives a pair of pants decomposition of any such surface when there are small necks, cutting the surf...
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作者：Bessis, David
摘要：Let V be a finite dimensional complex vector space and W subset of GL( V) be a finite complex reflection group. Let V-reg be the cornplemrnent in V of the reflecting hyperplanes. We prove that Vreg is a K(pi, 1) space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection groups. The complexified real case follows from a theorem of Deligne and, after contributions by Nakamura and Orlik-Solomon, only six exceptional cases remained open. In...
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作者：Bourgain, Jean; Demeter, Ciprian
摘要：We prove the l(2) Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete Restriction Conjecture, which implies the full range of expected L-x,t(p) Strichartz estimates for both the rational and (up to N-epsilon losses) the irrational torus. Another one is an improvement in the range for the discrete restriction theorem for lattice points on...
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作者：Buch, Anders Skovsted
摘要：We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks to the equivariant version of the 'quantum equals classical' result, our formula specializes to a L...
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作者：Colding, Tobias Holck; Minicozzi, William P., II
摘要：Once one knows that singularities occur, one naturally wonders what the singularities are like. For minimal varieties the first answer, already known to Federer-Fleming in 1959, is that they weakly resemble cones. For mean curvature flow, by the combined work of Huisken, Ilmanen, and White, singularities weakly resemble shrinkers. Unfortunately, the simple proofs leave open the possibility that a minimal variety or a mean curvature flow looked at under a microscope will resemble one blowup, bu...
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作者：Kahn, Jeremy; Markovic, Vladimir
摘要：We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces. (Good pants are pairs of pants whose cuffs have the length nearly equal to some large number R > 0.) Combined with our previous work on the Surface Subgroup Theorem, this yields a proof of the Ehrenpreis Conjecture.
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作者：To, Wing-Keung; Yeung, Sai-Kee
摘要：We show that the base complex manifold of an effectively parametrized holomorphic family of compact canonically polarized complex manifolds admits a smooth invariant Finsler metric whose holomorphic sectional curvature is bounded above by a negative constant. As a consequence, we show that such a base manifold is Kobayashi hyperbolic.
