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作者：Kozlovski, O.; Shen, W.; van Strien, S.
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作者：Avila, Artur; Forni, Giovanni
摘要：We prove that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a typical translation surface of genus g >= 2 (with prescribed singularity types) is weakly mixing.
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作者：Bezrukavnikov, Roman; Ginzburg, Victor
摘要：In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra a are controlled by the second Hochschild cohomology group of a. More generally, any n-parameter first order deformation of a gives, due to commutativity of the cup-product on Hochschild cohomology, a graded algebra morphism Sym(center dot)(k(n)) -> Ext(a-bimod)(2 center dot)(a, a). We prove that any extension of the n-parameter first order deformation of a to an infinite order formal deformation ...
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作者：Epstein, Charles L.
摘要：Let X be a compact Kahler manifold with strictly pseudoconvex boundary, Y. In this setting, the Spin(C) Dirac operator is canonically identified with partial derivative + partial derivative : C-infinity (X; Lambda(0,e)) -> C-infinity (X; Lambda(0,o)) . We consider modifications of the classical partial derivative-Neumann conditions that define Fredholm problems for the Spin(C) Dirac operator. In Part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these boundary value...
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作者：Kozlovski, O.; Shen, W.; Van Strien, S.
摘要：We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom A conjecture in real one-dimensional dynamics.
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作者：Field, Michael; Melbourne, Ian; Torok, Andrei
摘要：We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst C-r Axiom A flows, r >= 2, we show that there is a C-2-open, C-r-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds in a C-r, as opposed to Holder, topology.
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作者：Dugger, Daniel; Isaksen, Daniel C.
摘要：We settle an old question about the existence of certain 'sums-of-squares' formulas over a field F, related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must vanish. We prove that this result also holds over fields of characteristic p > 2.
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作者：Dostoglou, Stamatis; Salamon, Dietmar A.
摘要：We correct two mistakes in [1]. The first concerns the exponential decay in the proof of Theorem 7.4 and the second concerns the bubbling argument in the proof of Theorem 9.1.
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作者：Coates, Tom; Givental, Alexander
摘要：Given a holomorphic vector bundle E over a compact Kahler manifold X, one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : E -> X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H-0(Sigma, f*E) circle minus H-1(Sigma, f*E). Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theor...
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作者：Orlov, D.; Vishik, A.; Voevodsky, V.
