3期

最新文章

• The Alexander-Orbach conjecture holds in high dimensions AI翻译
  作者：Kozma, Gady; Nachmias, Asaf
  作者单位：Microsoft; Weizmann Institute of Science
  摘要：We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d > 6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d(s) = 4/3, that is, p(t)(x, x) = t(-2/3+o(1)). This establishes a conjecture of Alexander and Orbach (J. Phys. Lett. (Paris) 43:625-631, 1982). En route we calculate the o...
• An exact sequence for contact- and symplectic homology AI翻译
  作者：Bourgeois, Frederic; Oancea, Alexandru
  作者单位：Universite Libre de Bruxelles; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：A symplectic manifold W with contact type boundary M=a,W induces a linearization of the contact homology of M with corresponding linearized contact homology HC(M). We establish a Gysin-type exact sequence in which the symplectic homology SH(W) of W maps to HC(M), which in turn maps to HC(M), by a map of degree -2, which then maps to SH(W). Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization ...
• Semitoric integrable systems on symplectic 4-manifolds AI翻译
  作者：Pelayo, Alvaro; Ngoc, San Vu
  作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); Universite de Rennes
  摘要：Let (M, omega) be a symplectic 4-manifold. A semitoric integrable system on (M, omega) is a pair of smooth functions J, H is an element of C-infinity( M, R) for which J generates a Hamiltonian S-1-action and the Poisson brackets {J, H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our...
• Multiplicative rule of Schubert classes (vol 159, pg 407, 2005) AI翻译
  作者：Duan, Haibao; Zhao, Xuezhi
  作者单位：Chinese Academy of Sciences; Capital Normal University
• The contact invariant in sutured Floer homology AI翻译
  作者：Honda, Ko; Kazez, William H.; Matic, Gordana
  作者单位：University of Southern California; University System of Georgia; University of Georgia
  摘要：We describe an invariant of a contact 3-manifold with convex boundary as an element of Juhasz's sutured Floer homology. Our invariant generalizes the contact invariant in Heegaard Floer homology in the closed case, due to Ozsvath and SzabA(3).
• The Lee-Yang and Polya-Schur programs. I. Linear operators preserving stability AI翻译
  作者：Borcea, Julius; Branden, Petter
  作者单位：Royal Institute of Technology; Stockholm University
  摘要：In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probability theory, combinatorics, and matrix theory. We characterize all linear operators on finite or infinite-dimensional spaces of multivariate polynomials preserving the property of being non-vanishing whenever the variables are in prescribed open circu...
• A theorem of Tits type for compact Kahler manifolds AI翻译
  作者：Zhang, De-Qi
  作者单位：National University of Singapore
  摘要：We prove a theorem of Tits type about automorphism groups for compact Kahler manifolds, which has been conjectured in the paper [9].
• Serre's modularity conjecture (II) AI翻译
  作者：Khare, Chandrashekhar; Wintenberger, Jean-Pierre
  作者单位：Utah System of Higher Education; University of Utah; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：We provide proofs of Theorems 4.1 and 5.1 of Khare and Wintenberger (Invent. Math., doi: 10.1007/s00222-009-0205-7, 2009).
• Faltings heights of CM cycles and derivatives of L-functions AI翻译
  作者：Bruinier, Jan Hendrik; Yang, Tonghai
  作者单位：Technical University of Darmstadt; University of Wisconsin System; University of Wisconsin Madison
  摘要：We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.
• The quantum McKay correspondence for polyhedral singularities AI翻译
  作者：Bryan, Jim; Gholampour, Amin
  作者单位：University of British Columbia; California Institute of Technology
  摘要：Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity a,(3)/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over th...