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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...
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作者：Parnovski, Leonid; Shterenberg, Roman
作者单位：University of London; University College London; University of Alabama System; University of Alabama Birmingham
摘要：We prove the complete asymptotic expansion of the integrated density of states of a two-dimensional Schrodinger operator with a smooth periodic potential.
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作者：Fock, V. V.; Goncharov, A. B.
作者单位：National Research Centre - Kurchatov Institute; Alikhanov Institute for Theoretical & Experimental Physics; Brown University
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作者：Graczyk, Jacek; Smirnov, Stanislav
作者单位：Universite Paris Saclay; University of Geneva
摘要：We say that a rational function F satisfies the summability condition with exponent a if for every critical point c which belongs to the Julia set J there exists a positive integer n(c) so that Sigma(infinity)(n=1) vertical bar(F-n)'(F-nc(C))vertical bar(-alpha) < infinity and F has no parabolic periodic cycles. Let mu(max) be the maximal multiplicity of the critical points. The objective is to study the Poincare series for a large class of rational maps and establish ergodic and regularity pr...
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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 ...
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作者：Pandharipande, R.; Thomas, R. P.
作者单位：Imperial College London; Princeton University
摘要：For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs (C,D) where CaS,X is an embedded curve and DaS,C is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of X. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of X. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossi...
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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...
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作者：Levine, M.; Pandharipande, R.
作者单位：Northeastern University; Princeton University
摘要：We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary, the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo doubl...
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作者：Einsiedler, M.; Margulis, G.; Venkatesh, A.
作者单位：University System of Ohio; Ohio State University; Yale University; Stanford University
摘要：We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient group). The proofs make extensive use of spectral gaps, and also of a closing lemma for such actions.
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作者：Ni, Yi
作者单位：Massachusetts Institute of Technology (MIT)
