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作者：Lau, Eike; Nicole, Marc-Hubert; Vasiu, Adrian
摘要：The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field of characteristic p is the least positive integer m such that D[p(m)] determines D up to isomorphism (resp. up to isogeny). We show that these invariants are lower semicontinuous in families of p-divisible groups of constant Newton polygon. Thus they allow refinements of Newton polygon strata. In each isogeny class of p-divisible groups, we determine the maximal value of isogeny cutoffs an...
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作者：Ioana, Adrian; Popa, Sorin; Vaes, Stefaan
摘要：We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely remembers the group G. More precisely, if L(G) is isomorphic to the von Neumann algebra L Lambda of an arbitrary countable group Lambda, then Lambda must be isomorphic to G. This represents the first superrigidity result pertaining to group von Neumann algebras.
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作者：Chatterjee, Sourav
摘要：It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent chi and the wandering exponent are related through the universal relation chi = 2 xi - 1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.
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作者：Bonk, Mario; Merenkov, Sergei
摘要：We prove that every quasisymmetric self-homeomorphism of the standard 1/3-Sierpinski carpet S-3 is a Euclidean isometry. For carpets in a more general family, the standard 1/p-Sierpinski carpets S-p, p >= 3 odd, we show that the groups of quasisymmetric self-maps are finite dihedral. We also establish that S-p and S-q are quasisymmetrically equivalent only if p = q. The main tool in the proof for these facts is a new invariant-a certain discrete modulus of a path family-that is preserved under...
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作者：Sorensen, Claus M.
摘要：This paper contains a proof of a conjecture of Breuil and Schneider, on the existence of an invariant norm on any locally algebraic representation of GL(n), with integral central character, whose smooth part is given by a generalized Steinberg representation. In fact, we prove the analogue for any connected reductive group G. This is done by passing to a global setting, using the trace formula for an R-anisotropic model of G. The ultimate norm comes from classical p-adic modular forms.
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作者：Giulietti, P.; Liverani, C.; Pollicott, M.
摘要：We study the Ruelle and Selberg zeta functions for C-r Anosov flows, r > 2, on a compact smooth manifold. We prove several results, the most remarkable being (a) for C-infinity flows the zeta function is meromorphic on the entire complex plane; (b) for contact flows satisfying a bunching condition (e.g., geodesic flows on manifolds of negative curvature better than 1/9-pinched), the zeta function has a pole at the topological entropy and is analytic in a strip to its left; (c) under the same h...
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作者：Hassett, Brendan; Hyeon, Donghoon
摘要：We give a geometric invariant theory (GIT) construction of the log canonical model M-9(alpha) of the pairs (M-9,M- alpha delta) for alpha is an element of (7/10 epsilon, 7/10] for small epsilon is an element of Q(+) . We show that M-g (7/10-epsilon) is isomorphic to the GIT quotient of the Chow variety of bicanonical curves; M-g (7/10-epsilon) is isomorphic to the GIT quotient of the asymptotically-linearized Hilbert scheme of bicanonical curves. In each case, we completely classify the (semi)...
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作者：Cisinski, Denis-Charles
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作者：Avila, Artur; Gouezel, Sebastien
摘要：We consider the SL(2; R) action on moduli spaces of quadratic differentials. If mu is an SL(2; R)-invariant probability measure, crucial information about the associated representation on L-2(mu) (and, in particular, fine asymptotics for decay of correlations of the diagonal action, the Teichmuller flow) is encoded in the part of the spectrum of the corresponding foliated hyperbolic Laplacian that lies in (0, 1/4) (which controls the contribution of the complementary series). Here we prove tha...
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作者：Panchenko, Dmitry
摘要：In this paper we prove that the support of a random measure on the unit ball of a separable Hilbert space that satisfies the Ghirlanda-Guerra identities must be ultrametric with probability one. This implies the Parisi ultrametricity conjecture in mean-field spin glass models, such as the Sherrington-Kirkpatrick and mixed p-spin models, for which Gibbs measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.
