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作者：Kajino, Naotaka; Murugan, Mathav
作者单位：Kobe University; Kyoto University; University of British Columbia
摘要：We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric Dirichlet space in which every metric ball has compact closure (MMD space), the finiteness of the conformal walk dimension characterizes the conjunction of the metric doubling property and the elliptic Harnack inequality. Roughly speaking, the conformal walk dimensi...
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作者：Nakamura, Kentaro
作者单位：Saga University
摘要：In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's zeta morphisms for Galois representations associated to Hecke eigen cusp newforms. The existence of such morphisms was predicted by Kato's generalized Iwasawa main conjecture. Based on Kato's original construction, we construct our zeta morphisms using many de...
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作者：Filonov, Nikolay; Levitin, Michael; Polterovich, Iosif; Sher, David A.
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; University of Reading; Universite de Montreal; DePaul University
摘要：The celebrated Polya's conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl's asymptotics. Polya's conjecture is known to be true for domains which tile Euclidean space, and, in addition, for some special domains in higher dimensions. In this paper, we prove Polya's conjecture for the disk, making it the first non-...
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作者：Fei, Mingwen; Lin, Fanghua; Wang, Wei; Zhang, Zhifei
作者单位：Anhui Normal University; New York University; Zhejiang University; Peking University
摘要：In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: partial derivative(t)A = Delta A - epsilon(-2) (AA(T)A - A) with A: Omega subset of R-m -> R-nxn. We show that the sharp interface system is a two-phases flow system: the interface evolves according to the motion by mean curvature; in the two bulk phase regions, the solution obeys the heat flow of harmonic maps with values in O+(n) and O-(n) (represent the sets of n u n orthogonal...
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作者：Labourie, Francois; Toulisse, Jeremy
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：We study in this paper quasiperiodic maximal surfaces in pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. We show that the limit curves of these surfaces in the Einstein Universe admits a canonical quasisymmetric parametrisation, while conversely every quasisymmetric curve in the Einstein Universe bounds a quasiperiodic surface in such a way that the quasisymmetric parametrisation is a continuous extension ...
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作者：Gunningham, Sam; Jordan, David; Safronov, Pavel
作者单位：Montana State University System; Montana State University Bozeman; University of Edinburgh; University of Zurich
摘要：We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that skein modules of closed 3-manifolds are finite-dimensional, resolving in the affirmative a conjecture of Witten.
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作者：Guo, Yan; Pausader, Benoit; Widmayer, Klaus
作者单位：Brown University; University of Zurich; University of Vienna
摘要：We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform rigid body rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis...
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作者：Laba, Izabella; Londner, Itay
作者单位：University of British Columbia; Weizmann Institute of Science
摘要：It is well known that if a finite set A subset of Z tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A circle plus B = Z(M) of a finite cyclic group. We are interested in characterizing all finite sets A subset of Z that have this property. Coven and Meyerowitz (J Algebra 212:161-174, 1999) proposed conditions (T1), (T2) that are sufficient for A to tile, and necessary when the cardinality of A has at most two di...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider directed polymers in random environment in the critical dimension d = 2, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at criticality, the diffu-sively rescaled random field of partition functions has a unique scaling limit: a universal process of random measures on R-2 with logarithmic correlations, which we call the Critical 2d Stochastic Heat Flow. It is the natural candidate for the long sought solution of the critical ...
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作者：Peled, Ron; Spinka, Yinon
作者单位：Tel Aviv University; University of British Columbia
摘要：A proper q-coloring of a domain in Z(d) is a function assigning one of q colors to each vertex of the domain such that adjacent vertices are colored differently. Sampling a proper q-coloring uniformly at random, does the coloring typically exhibit long-range order? It has been known since the work of Dobrushin that no such ordering can arise when q is large compared with d. We prove here that long-range order does arise for each q when d is sufficiently high, and further characterize all perio...
