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作者：Vasy, Andras
摘要：We correct an error in the proof of Proposition 7.3 of the author's paper on the propagation of singularities for the wave equation on manifolds with corners. The correction does not affect the statement of Proposition 7.3, and it does not affect any other part of the paper.
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作者：Greene, Joshua Evan
摘要：We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups. This leads to sharp information about the genus of such a knot. The arguments rely on tools from Floer homology and lattice theory. They are primarily combinatorial in nature.
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作者：Branson, Thomas P.; Fontana, Luigi; Morpurgo, Carlo
摘要：We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CR-pluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequality in the form given by Carlen and Loss.
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作者：Juschenko, Kate; Monod, Nicolas
摘要：We provide the first examples of finitely generated simple groups that are amenable (and infinite). To this end, we prove that topological full groups of minimal systems are amenable. This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.
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作者：Eskin, Alex; Fisher, David; Whyte, Kevin
摘要：In this paper we prove quasi-isometric rigidity results concerning lattices in Sol and lamplighter groups. The paper builds in a substantial way on our earlier paper Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs.
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作者：Neves, Andre
摘要：Given any embedded Lagrangian on a four-dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class that develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lagrangian mean curvature flow.
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作者：Young, Robert
摘要：We prove that when n >= 5, the Dehn function of SL(n; Z) is quadratic. The proof involves decomposing a disc in SL(n; R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n; Z) and replacing large elementary matrices by shortcuts, we obtain words of a particular form, and we use combinatorial techniques to fill these loops.
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作者：Odaka, Yuji
摘要：We prove that various GIT semistabilities of polarized varieties imply semi-log-canonicity.
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作者：Heinloth, Jochen; Ngo, Bao-Chau; Yun, Zhiwei
摘要：Deligne constructed a remarkable local system on P-1 - {0, infinity} attached to a family of Kloosterman sums. Katz calculated its monodromy and asked whether there are Kloosterman sheaves for general reductive groups and which automorphic forms should be attached to these local systems under the Langlands correspondence. Motivated by work of Gross and Frenkel-Gross we find an explicit family of such automorphic forms and even a simple family of automorphic sheaves in the framework of the geom...
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作者：Benoist, Yves; Quint, Jean-Francois
摘要：Let G be a real Lie group, A be a lattice in G and F be a compactly generated closed subgroup of G. If the Zariski closure of the group Ad(F) is semisimple with no compact factor, we prove that every Gamma-orbit closure in G/Lambda is a finite volume homogeneous space. We also establish related equidistribution properties.
