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作者：Evseev, Anton; Kleshchev, Alexander
摘要：We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like 'local' objects, which replace wreath products of Brauer tree algebras in the context of the Broue abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath produ...
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作者：Mirkovic, I.; Vilonen, K.
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作者：Eskin, Alex; Filip, Simion; Wright, Alex
摘要：We compute the algebraic hull of the Kontsevich Zorich cocycle over any GL(2)(+) (R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
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作者：Liokumovich, Yevgeny; Marques, Fernando C.; Neves, Andre
摘要：Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum {omega(Rho)(M)}(p is an element of N) satisfies a Weyl law that was conjectured by Gromov.
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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...
