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作者：Goldbring, Isaac
摘要：We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model our solution after a treatment of Hilbert's fifth problem for global groups by Hirschfeld.
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作者：de Cataldo, Mark Andrea A.; Migliorini, Luca
摘要：We describe the perverse filtration in cohomology using the Lefschetz hyperplane theorem.
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作者：Aizenbud, Avraham; Gourevitch, Dmitry; Rallis, Stephen; Schiffmann, Gerard
摘要：In the local, characteristic 0, non-Archimedean case, we consider distributions on GL(n + 1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL(n + 1) to GL(n). Similar theorems are obtained for orthogonal or unitary groups.
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作者：Briskin, Miriam; Roytvarf, Nina; Yomdin, Yosef
摘要：An Abel differential equation y' = p (x) y(2) + q(x) y(3) is said to have a center at a set A = {a(1),...,a(r)} of complex numbers if y(a(1)) = y(a(2)) = ... = y (a(r)) for any solution y(x) (with the initial value y(a(1)) small enough). The polynomials p, q are said to satisfy the Polynomial Composition Condition on A if there exist polynomials P, Q and W such that P D R p and Q D R q are representable as P(x) = (P) over tilde (W(x)), Q(x) = (Q) over tilde (W(x)), and W(a(1)) = W(a(2)) = ... ...
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作者：Burns, Keith; Wilkinson, Amie
摘要：Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C-2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satisfied in particular by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C1+delta partially hyperbolic systems.
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作者：Fouvry, Etienne; Klueners, Juergen
摘要：We give asymptotic upper and lower bounds for the number of squarefree d (0 < d <= X) such that the equation x(2) - dy(2) = -1 is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm -1 and give strong evidence in the direction of a conjecture due to P. Stevenhagen.
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作者：Contreras, Gonzalo
摘要：We prove a perturbation lemma for the derivative of geodesic flows in high dimension. This implies that a C-2 generic riemannian metric has a nontrivial hyperbolic basic set in its geodesic flow.
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作者：Soundararajan, Kannan
摘要：We describe a general method to obtain weak subconvexity bounds for many classes of L-functions. We give several examples of our bound, and our work has applications to a conjecture of Rudnick and Sarnak for the mass equidistribution of Hecke eigenforms
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作者：Hochman, Michael; Meyerovitch, Tom
摘要：We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number h >= 0 is the entropy of such an SFT if and only if it is right recursively enumerable, i.e. there is a computable sequence of rational numbers converging to h from above. The same characterization holds for the entropies of sofic shifts. On the other hand, the entropy of strongly irreducible SFTs is computable.
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作者：Burago, Dmitri; Ivanov, Sergei
摘要：We say that a Riemannian manifold (M, g) with a non-empty boundary partial derivative M is a minimal orientable filling if, for every compact orientable. ((M) over tilde, (g) over tilde) with partial derivative(M) over tilde = partial derivative M, the inequality d((g) over tilde)(x, y) >= d(g)(x, y) for all x, y is an element of partial derivative M implies vol((M) over tilde, (g) over tilde) >= vol(M, g). We show that if a metric g on a region M subset of R-n with a connected boundary is suf...
