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作者：Bate, M; Martin, B; Röhrle, G
作者单位：University of Birmingham; University of Canterbury
摘要：Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert-Mumford-Kempf from geometric invariant theory. We deduce that a normal subgroup of a G-completely reducible subgroup of G is again G-completely reducible, ...
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作者：Buzzi, J
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
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作者：Goodman-Strauss, C
作者单位：University of Arkansas System; University of Arkansas Fayetteville
摘要：We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a regular production system [5] that does admit bi-infinite orbits, but admits no periodic orbits.
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作者：Arapura, D
作者单位：Purdue University System; Purdue University
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作者：Jelonek, Z
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：Let K be an algebraically closed field and let X subset of K-m be an n-dimensional affine variety. Assume that f(1),..., f(k) are polynomials which have no common zeros on X. We estimate the degrees of polynomials A(i) is an element of K[X] such that 1 = Sigma(k)(i=1) A(i) f(i) n X. Our estimate is sharp for k <= n and nearly sharp for k > n. Now assume that f(1),..., f(k) are polynomials on X. Let I = (f(1),..., f(k)). K[X] be the ideal generated by fi. It is well-known that there is a number...
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作者：van den Ban, EP; Schlichtkrull, H
作者单位：Utrecht University; University of Copenhagen; Aarhus University
摘要：We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized Eisenstein integrals and of the Maass-Selberg relations satisfied by...
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作者：Eskin, A; Mozes, S; Oh, H
作者单位：University of Chicago; Hebrew University of Jerusalem; Princeton University; Institute for Advanced Study - USA
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作者：Burq, N; Gérard, P; Tzvetkov, N
作者单位：Universite Paris Saclay
摘要：We study the cubic non linear Schrodinger equation (NLS) on compact surfaces. On the sphere S-2 and more generally on Zoll surfaces, we prove that, for s > 1/4, NLS is uniformly well-posed in H-s, which is sharp on the sphere. The main ingredient in our proof is a sharp bilinear estimate for Laplace spectral projectors on compact surfaces.
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作者：Belolipetsky, M; Lubotzky, A
作者单位：Hebrew University of Jerusalem; Russian Academy of Sciences
摘要：The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n >= 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n=2 and n=3 have been proven by Greenberg (1974) and Kojima (1988), respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to show that such manifolds exist.
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作者：Oh, YG; Park, JS
作者单位：University of Wisconsin System; University of Wisconsin Madison; Korea Institute for Advanced Study (KIAS)
摘要：In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs C-infinity deformations of coisotropic submanifolds and define the corresponding C-infinity-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. This is a non-commutative and non-linear generalization of the well-known description of the local deformation space of Lagrangian submanifolds as the set of graphs of closed one forms in the Darbou...
