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作者：Beliakova, Anna; Buehler, Irmgard; Le, Thang
作者单位：University of Zurich; University System of Georgia; Georgia Institute of Technology
摘要：Given a rational homology 3-sphere M with |H (1)(M,acurrency sign)|=b and a link L inside M, colored by odd numbers, we construct a unified invariant I (M,L) belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L=a..., I (M) coincides with Habiro's invariant of integral homology 3-spheres. For b > 1, the unified invariant defined by the third author is de...
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作者：Peterson, Jesse; Thom, Andreas
作者单位：Leipzig University; Vanderbilt University
摘要：In this article we study cocycles of discrete countable groups with values in l(2)G and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l(2)G and answer several questions from De Cornulier et al. (Transform. Groups 13(1): 125-147, 2008). Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first l(2)-Betti number. We give numerous applications a...
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作者：Duplantier, Bertrand; Sheffield, Scott
作者单位：CEA; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Massachusetts Institute of Technology (MIT)
摘要：Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2 pi)(-1) integral(D) del h(z) . del h(z)dz, and a constant 0 <= gamma < 2. The Liouville quantum gravity measure on D is the weak limit as epsilon -> 0 of the measures epsilon(gamma 2/2)e(gamma h epsilon(z)) dz, where dz is Lebesgue measure on D and h(epsilon)(z) denotes the mean value of h on the circle of radius epsilon centered at z. Given a random (or deterministic) subset X of D one ...
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作者：Meyerovitch, Tom
摘要：We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson (A strange two-dimensional symbolic system, 1992), we show that growth complexities of the form exp (n (alpha+o(1))) are possible for non-integer alpha's. In terminology of de Carvalho (Port. Math. 54(1):19-40, 1997), such subshifts have entropy dimension alpha. The class...
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作者：Navarro, Gabriel; Tiep, Pham Huu
作者单位：University of Arizona; University of Valencia
摘要：The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.
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作者：Auscher, Pascal; Axelsson, Andreas
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Australian National University; Linkoping University
摘要：We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with L (2) boundary data. The coefficients A may depend on all variables, but are assumed to be close to coefficients A (0) that are independent of the coordinate transversal to the boundary, in the Carleson sense aEuro-A-A (0)aEuro- (C) defined by Dahlberg. We obtain a number of a priori estimates and boundary behaviour results under finiteness of aEuro-A-A (0)aEuro-...
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作者：Chen, Jungkai Alfred; Hacon, Christopher D.
作者单位：Utah System of Higher Education; University of Utah; National Taiwan University
摘要：Let f:X -> Y be an algebraic fiber space with general fiber F. If Y is of maximal Albanese dimension, we show that kappa(X)a parts per thousand yen kappa(Y)+kappa(F).
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作者：Le Rousseau, Jerome; Robbiano, Luc
作者单位：Universite de Orleans; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In (0, T) x Omega, Omega open subset of R-n, n >= 2, we consider a parabolic operator P = partial derivative(t) - del(x)delta(t, x)del(x), where the ( scalar) coefficient delta(t, x) is piecewise smooth in space yet discontinuous across a smooth interface S. We prove a global in time, local in space Carleman estimate for P in the neighborhood of any point of the interface. The observation region can be chosen independently of the sign of the jump of the coefficient d at the considered point. T...
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作者：Duchin, Moon; Leininger, Christopher J.; Rafi, Kasra
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign; University of Oklahoma System; University of Oklahoma - Norman
摘要：In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics. The geometric interpretation is that flat metrics deg...
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作者：Figalli, A.; Maggi, F.; Pratelli, A.
作者单位：University of Texas System; University of Texas Austin; University of Florence; University of Pavia
摘要：A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov's proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.
