-
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...
-
作者：Blomer, Valentin
摘要：Strong bounds-going beyond Sarnak's density hypothesis-are obtained for the number of automorphic forms for the group Gamma(0)(q) subset of SL(n, Z) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for GL(n). Further applications are given.
-
作者：Kim, Dongryul M.; Oh, Hee
作者单位：Yale University; Korea Institute for Advanced Study (KIAS)
摘要：Let Gamma < PSL2( C) similar or equal to Isom(+) (H-3) be a finitely generated non-Fuchsian Kleinian group whose ordinary set Omega = S-2 - Lambda has at least two components. Let rho : Gamma -> PSL2( C) be a faithful discrete non-Fuchsian representation with boundary map f : Lambda -> S-2 on the limit set. In this paper, we obtain a new rigidity theorem: if f is conformal on Lambda, in the sense that f maps every circular slice of Lambda into a circle, then f extends to a Mobius transformatio...
-
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 ...
-
作者：Canzani, Yaiza; Galkowski, Jeffrey
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of London; University College London
摘要：We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold (M, g) of dimension n, let H(lambda )denote the kernel of the spectral projector for the Laplacian, (1)[0,lambda(2)](-delta(g)). Assuming only that the set of near periodic geodesics over W subset of M has small measure, we prove that as lambda -> infinity integral(W) Pi(lambda) (x, x)dx = (2 pi)(-n) vol(R)(n)(B) volg(W) lambda(n) + O (lambda(n-1...
-
作者：Pstragowski, Piotr
作者单位：Harvard University
摘要：To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a product-preserving sheaf on the site of finite spectra with projective E-homology. We show that the infinity-category SynE of synthetic spectra based on E is in a precise sense a deformation of the infinity-category of spectra into quasi-coherent sheaves over a certain algebraic stack, and show that this deformation encodes the E*-based Adams spectral sequence. We describe a symmetric monoidal functor f...
-
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...
-
作者：Guralnick, Robert M.; Larsen, Michael; Tiep, Pham Huu
作者单位：University of Southern California; Indiana University System; Indiana University Bloomington; Rutgers University System; Rutgers University New Brunswick
摘要：The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to vertical bar G vertical bar in a logarithmic sense.
-
作者：Kozlowski, Karol K.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：This paper develops a technique allowing one to prove the convergence of a class of series of multiple integrals which corresponds to the form factor expansion of space-like separated two-point functions in the 1+1 dimensional massive integrable Sinh-Gordon quantum field theory.
-
作者：Berczi, Gergely; Kirwan, Frances
作者单位：Aarhus University; University of Oxford
摘要：The Green-Griffiths-Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang.
