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作者：Brosnan, Patrick; Reichstein, Zinovy; Vistoli, Angelo
摘要：We prove that the essential dimension of the spinor group Spin, grows exponentially with 17 and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more complex, in high dimensions, than previously expected.
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作者：Lauret, Jorge
摘要：We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has shown that under a simple algebraic condition (he calls such a solvmanifold standard), Einstein solvmanifolds have many remarkable structural and uniqueness properties. In this paper, we prove that any Einstein solvmanifold is standard, by applying a stratification procedure adapted from on...
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作者：Le Roux, Frederic
摘要：We study the dynamics of surface homeomorphisms around isolated fixed points whose Poincare-Lefschetz index is not equal to 1. We construct a new conjugacy invariant, which is a cyclic word on the alphabet {up arrow, ->, down arrow, <-}. This invariant is a refinement of the P.-L. index. It can be seen as a canonical decomposition of the dynamics into a finite number of sectors of hyperbolic, elliptic or indifferent type. The contribution of each type of sector to the P.-L. index is respective...
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作者：Schramm, Oded; Steif, Jeffrey E.
摘要：One goal of this paper is to prove that dynamical critical site percolation on the planar triangular lattice has exceptional times at which percolation occurs. In doing so, new quantitative noise sensitivity results for percolation are obtained. The latter is based on a novel method for controlling the level k Fourier coefficients via the construction of a randomized algorithm which looks at random bits, outputs the value of a particular function but looks at any fixed input bit with low proba...
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作者：Kamnitzer, Joel
摘要：We give an explicit description of the Mirkovie-Vilonen cycles on the affine Grassmannian for arbitrary complex reductive groups. We also give a combinatorial characterization of the MV polytopes. We prove that a polytope is an MV polytope if and only if it is a lattice polytope whose defining hyperplanes are parallel to those of the Weyl polytopes and whose 2-faces are rank 2 MV polytopes. As an application, we give a bijection between Lusztig's canonical basis and the set of MV polytopes.
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作者：Smirnov, Stanislav
摘要：We construct discrete holomorphic fermions in the random cluster Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequels those observables are used to construct conformally invariant scaling limits of interfaces and identify those with Schramm's SLE curves. Though the critical Ising model is often cited as a classical example of conformal invariance, it seems that ours is the first paper where it is actually...
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作者：Eliasson, L. Hakan; Kuksin, Sergei B.
摘要：We consider the d-dimensional nonlinear Schrodinger equation under periodic boundary conditions: -i(u) over dot = -Delta u + V(x) *u + epsilon partial derivative F/partial derivative(u) over bar (x, u, (u) over bar), u = u(t, x), x is an element of Td where V(x) = Sigma(V) over cap (a)e(i < a, x >) is an analytic function with (V) over cap real, and F is a real analytic function in Ru, Ju and x. (This equation is a popular model for the 'real' NLS equation, where instead of the convolution ter...
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作者：Bowen, Lewis Phylip
摘要：This paper introduces a new measure-conjugacy invariant for actions of free groups. Using this invariant, it is shown that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy. This answers a question of Ornstein and Weiss.
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作者：Etingof, Pavel; Henriques, Andre; Kamnitzer, Joel; Rains, Eric M.
摘要：We compute the Poincare polynomial and the cohomology algebra with rational coefficients of the manifold M-n of real points of the moduli space of algebraic curves of genus 0 with n labeled points. This cohomology is a quadratic algebra, and we conjecture that it is Koszul. We also compute the 2-local torsion in the cohomology of M-n. As was shown by the fourth author, the cohomology of M-n does not have odd torsion, so that the above determines the additive structure of the integral homology ...
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作者：Caffarelli, Luis A.; Vasseur, Alexis
摘要：Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L-2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L-2 data and critical diffusion. (-Delta)(1/2) are locally smooth for any space dimension.
