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作者：Frohman, Charles; Meeks, William H., III
摘要：We give a complete topological classification of properly embedded minimal surfaces in Euclidian three-space.
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作者：Caffarelli, Luis A.; Gutierrez, Cristian E.; Huang, Qingbo
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作者：Rudelson, Mark
摘要：Let A be an n x n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A(-1) does not exceed Cn(3/2) with probability close to 1.
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作者：Helfgott, H. A.
摘要：We show that every subset of SL2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL2(Z/pZ), every element of SL2(Z/pZ) can be expressed as a product of at most O((logp)(c)) elements of A boolean OR A(-1), where c and the implied constant are absolute.
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作者：Bezrukavnikov, Roman; Mirkovic, Ivan; Rumynin, Dmtriy
摘要：We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. The first step is to observe that the derived functor of global sections provides an equivalence between the derived category of D-modules (with no divided powers) on the flag var...
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作者：Behrstock, Jason A.; Minsky, Yair N.
摘要：We study the large scale geometry of the mapping class group, MCG(S). Our main result is that for any asymptotic cone of MCG(S), the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG(S). An application is a proof of Brock-Farb's Rank Conjecture which asserts that MCG(S) has quasi-flats of dimension N if and only if it has a rank N free abelian subgroup. (Hamenstadt has also given a proof of this conjecture, using different methods.) W...
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作者：Fernandez, Marisa; Munoz, Vicente
摘要：We answer in the affirmative the question posed by Babenko, and Taimanov [3] on the existence of nonformal, simply connected, compact symplectic manifolds of dimension 8.
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作者：Bhargava, Manjul
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作者：Vasy, Andras
摘要：In this paper we describe the propagation of C-infinity and Sobolev singularities for the wave equation on C-infinity manifolds with corners M equipped with a Riemannian metric g. That is, for X = M x R-t, P = D-t(2) - Delta(M), and u is an element of H-loc(1) (X) solving Pu = 0 with homogeneous Dirichlet or Neumann boundary conditions, we show that WFb(u) is a union of maximally extended generalized broken bicharacteristics. This result is a C-infinity counterpart of Lebeau's results for the ...
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作者：Mirzakhani, Maryam
