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作者：Tsimerman, Jacob
摘要：We prove the existence of an abelian variety A of dimension g over (Q) over bar that is not isogenous to any Jacobian, subject to the necessary condition g > 3. Recently, C. Chai and F. Oort gave such a proof assuming the Andre-Oort conjecture. We modify their proof by constructing a special sequence of CM points for which we can avoid any unproven hypotheses. We make use of various techniques from the recent work of Klingler-Yafaev et al.
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作者：Abouzaid, Mohammed
摘要：In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere. More precisely, we prove that such an exotic sphere cannot embed as a Lagrangian in the cotangent bundle of the standard sphere. The main ingredients of the construction are (1) the fact that the graph of the Hopf fibration embeds the standard sphere, and hence any Lagrangian which em...
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作者：Eyssidieux, P.; Katzarkov, L.; Pantev, T.; Ramachandran, M.
摘要：In this paper we settle affirmatively Shafarevich's uniformization conjecture for varieties with linear fundamental groups. We prove the strongest to date uniformization result - the universal covering space of a complex projective manifold with a linear fundamental group is holomorphically convex. The proof is based on both known and newly developed techniques in non-abelian Hodge theory.
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作者：Fernandez de Bobadilla, Javier; Pereira, Maria Pe
摘要：We prove that Nash mapping is bijective for any surface defined over an algebraically closed field of characteristic 0.
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作者：Chai, Ching-Li; Oort, Frans
摘要：We define a notion of Weyl CM points in the moduli space A(g,1) of g-dimensional principally polarized abelian varieties and show that the Andre-Oort conjecture (or the GRH) implies the following statement: for any closed subvariety X subset of(not equal) A(g,1) over Q(a), there exists a Weyl special point [(B, mu)] is an element of A(g,1)(Q(a)) such that B is not isogenous to the abelian variety A underlying any point [(A, lambda)] is an element of X. The title refers to the case when g >= 4 ...
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作者：Germain, P.; Masmoudi, N.; Shatah, J.
摘要：We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L-2 related norms, with dispersive estimates, which give decay in L-infinity. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
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作者：Alekseev, Anton; Torossian, Charles
摘要：The Kashiwara-Vergne (KV) conjecture is a property of the Campbell-Hausdorff series put forward in 1978. It has been settled in the positive by E. Meinrenken and the first author in 2006. In this paper, we study the uniqueness issue for the KV problem. To this end, we introduce a family of infinite-dimensional groups KRVn0, and a group KRV2 which contains KRVS20 as a normal subgroup. We show that KRV2 also contains the Grothendieck-Teichmuller group GRT(1) as a subgroup, and that it acts freel...
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作者：Sheffield, Scott; Werner, Wendelin
摘要：For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scaling limits of interfaces in models from statistical physics. This property is basically the combination of conformal invariance and the locality of the interaction in the model. Unlike the Markov property that Schramm used to characterize SLE curves (which involves conditioning on partially generated interfaces up to ...
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作者：Kahn, Jeremy; Markovic, Vladimir
摘要：Let M-3 be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M-3 so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.
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作者：McDuff, Dusa; Schlenk, Felix
摘要：This paper calculates the function c(a) whose value at a is the infimum of the size of a ball that contains a symplectic image of the ellipsoid E(1, a). (Here a >= 1 is the ratio of the area of the large axis to that of the smaller axis.) The structure of the graph of c(a) is surprisingly rich. The volume constraint implies that c(a) is always greater than or equal to the square root of a, and it is not hard to see that this is equality for large a. However, for a less than the fourth power ta...
