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作者：Nekrashevych, Volodymyr
摘要：We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.
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作者：Davison, Ben
摘要：Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew-symmetric quantum cluster algebras, via a proof of a conjecture first suggested by Kontsevich on the purity of mixed Hodge structures arising in the theory of cluster mutation of spherical collections in 3-Calabi Yau categories. The result implies positivity, as well as the stronger Lefschetz property conjectured by Efimov, and also the classical positivity conjectu...
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作者：Lawson, Tyler
摘要：The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown- Peterson spectrum does not admit the structure of an E-n-algebra for any n >= 12, answering a question of May in the negative.
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作者：Brendle, Simon
摘要：We present a new curvature condition that is preserved by the Ricci flow in higher dimensions. For initial metrics satisfying this condition, we establish a higher dimensional version of Hamilton's neck-like curvature pinching estimate. Using this estimate, we are able to prove a version of Perelman's Canonical Neighborhood Theorem in higher dimensions. This makes it possible to extend the flow beyond singularities by a surgery procedure in the spirit of Hamilton and Perelman. As a corollary, ...
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作者：Hillairet, Luc; Judge, Chris
摘要：We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degenerating family of triangles. In particular, we use a careful analysis of spectral projections near the crossings of these eigenvalue branches with the eigenvalue branches of a mode...
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作者：Isett, Philip
摘要：For any alpha < 1/3, we construct weak solutions to the 3D incompressible Euler equations in the class CtCx alpha that have nonempty, compact support in time on R x T-3 and therefore fail to conserve the total kinetic energy. This result, together with the proof of energy conservation for alpha > 1/3 due to [Eyink] and [Constantin, E, Titi], solves Onsager's conjecture that the exponent alpha = 1/3 marks the threshold for conservation of energy for weak solutions in the class (LtCx alpha)-C-in...
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作者：Logunov, Alexander
摘要：Let u be a harmonic function in the unit ball B(0, 1) subset of R-n, n >= 3, such that u(0) = 0. Nadirashvili conjectured that there exists a positive constant c, depending on the dimension n only, such that Hn-1 ({u = 0} boolean AND B ) >= c. We prove Nadirashvili's conjecture as well as its counterpart on C-infinity-smooth Riemannian manifolds. The latter yields the lower bound in Yau's conjecture. Namely, we show that for any compact C-infinity-smooth Riemannian manifold M (without boundary...
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作者：Bamler, Richard H.
摘要：In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension >= 4. We also establish a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. These results are based on a compactness theorem for Ricci flows with bounded scalar curvature, which states that any sequence of suc...
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作者：Balister, Paul; Bollobas, Bela; Morris, Robert
摘要：Consider a random sequence of N integers, each chosen uniformly and independently from the set {1,..., x}. Motivated by applications to factorization algorithms such as Dixon's algorithm, the quadratic sieve, and the number field sieve, Pomerance in 1994 posed the following problem: how large should N be so that, with high probability, this sequence contains a subsequence, the product of whose elements is a perfect square? Pomerance determined asymptotically the logarithm of the threshold for ...
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作者：Brown, Aaron; Hertz, Federico Rodriguez; Wang, Zhiren
摘要：In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices. Suppose Gamma is a lattice in a semisimple Lie group, all of whose factors have rank 2 or higher. Let a be alpha smooth Gamma-action on a compact nilmanifold M that lifts to an action on the universal cover. If the linear data rho of alpha contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of alpha and rho on a finite-index subgroup of Gamma. If alpha i...
