-
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.
-
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
-
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...
-
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...
-
作者：Pascal, Boyer
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor's book (The Geometry and Cohomology of Some Simple Shimura Varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, 2001), we describe the monodromy filtration of the vanishing cycles complex and the spectral sequence associated to it. We prove in particular that this filtration coincides with the weight one up to shift. Thanks to the Berkovich-Fargues' theorem, we deduce ...
-
作者：Mayboroda, Svitlana; Maz'ya, Vladimir
作者单位：Brown University; University System of Ohio; Ohio State University; University of Liverpool; Linkoping University
摘要：The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known about higher order elliptic equations in the general setting. In this paper we introduce new integral identities that allow to investigate the solutions to the biharmonic equation in an arbitrary domain. We establish: (1) boundedness of the gradie...
-
作者：Buch, Anders Skovsted; Kresch, Andrew; Tamvakis, Harry
作者单位：University System of Maryland; University of Maryland College Park; Rutgers University System; Rutgers University New Brunswick; University of Zurich
摘要：We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coef...
-
作者：Peterson, Jesse
作者单位：University of California System; University of California Berkeley
摘要：We introduce the notion of L (2)-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L (2)-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property I, or are weakly rigid. As a consequence we obtain that if M is a free product of diffuse von Neumann algebras, or if M=LI where I is a finitely gener...
-
作者：Braden, Tom; Proudfoot, Nicholas
作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of Oregon
摘要：We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice...
-
作者：Panin, Ivan; Pimenov, Konstantin; Roendigs, Oliver
作者单位：University of Bielefeld; 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; University Osnabruck
摘要：Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P-1-spectrum MGL of Voevodsky is considered as a commutative P-1-ring spectrum. Setting MGL(i) = circle plus(p-2q=i) MGL(p,q) we regard the bigraded theory MGL(p,q) as just a graded theory. There is a unique ring morphism phi: MGL(0)(k) -> Z which sends the class [X](MGL) of a smooth projective k-variety X to the Euler characteristic chi(X, O-X) of the...
