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作者：Vasy, Andras
作者单位：Stanford University
摘要：In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under perturbations. This framework, described in Sect. 2, resides on a compact manifold without boundary, hence in the standard setting of microlocal analysis. Many natural applications arise in the setting of non-Riemannian b-metrics in the context of Melrose's b-structures. These include asymptotically de...
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作者：Potapov, Denis; Skripka, Anna; Sukochev, Fedor
作者单位：University of New South Wales Sydney; University of New Mexico
摘要：This paper resolves affirmatively Koplienko's (Sib. Mat. Zh. 25:62-71, 1984) conjecture on existence of higher order spectral shift measures. Moreover, the paper establishes absolute continuity of these measures and, thus, existence of the higher order spectral shift functions. A spectral shift function of order naacenter dot is the function eta (n) =eta (n,H,V) such that for every sufficiently smooth function f, where H is a self-adjoint operator defined in a separable Hilbert space ai and V ...
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作者：Kakde, Mahesh
作者单位：University of London; King's College London
摘要：Let p be an odd prime. Let be a compact p-adic Lie group with a quotient isomorphic to acurrency sign (p) . We give an explicit description of K (1) of the Iwasawa algebra of in terms of Iwasawa algebras of Abelian subquotients of . We also prove a result about K (1) of a certain canonical localisation of the Iwasawa algebra of , which occurs in the formulation of the main conjectures of noncommutative Iwasawa theory. These results predict new congruences between special values of Artin L-func...
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作者：Clarke, Matthew C.; Premet, Alexander
作者单位：University of Cambridge; University of Manchester
摘要：Let G be a connected reductive algebraic group over an algebraically closed field of characteristic pa parts per thousand yen0. We give a case-free proof of Lusztig's conjectures (Lusztig in Transform. Groups 10:449-487, 2005) on so-called unipotent pieces. This presents a uniform picture of the unipotent elements of G which can be viewed as an extension of the Dynkin-Kostant theory, but is valid without restriction on p. We also obtain analogous results for the adjoint action of G on its Lie ...
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作者：Massot, Patrick; Niederkrueger, Klaus; Wendl, Chris
作者单位：Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of London; University College London
摘要：For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five), while also being obstructed by all known manifestations of overtwistedness. We also find the first examples of contact manifolds in all dimensions that are not symplectically fil...
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作者：Ovrelid, Nils; Vassiliadou, Sophia
作者单位：University of Oslo; Georgetown University
摘要：Let X be a pure n-dimensional (where na parts per thousand yen2) complex analytic subset in a, (N) with an isolated singularity at 0. In this paper we express the L (2)-(0,q)--cohomology groups for all q with 1a parts per thousand currency signqa parts per thousand currency signn of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L (2)-(0,q)--cohomology groups of the smooth points of X, in terms of resolution da...
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作者：Molev, A. I.
作者单位：University of Sydney
摘要：For each simple Lie algebra consider the corresponding affine vertex algebra at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of...
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作者：Hacon, Christopher D.; Xu, Chenyang
作者单位：Utah System of Higher Education; University of Utah
摘要：Let f:X -> U be a projective morphism of normal varieties and (X,Delta) a dlt pair. We prove that if there is an open set U (0)aS,U, such that (X,Delta)x (U) U (0) has a good minimal model over U (0) and the images of all the non-klt centers intersect U (0), then (X,Delta) has a good minimal model over U. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion...
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作者：Bellaiche, Joel
作者单位：Brandeis University
摘要：We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.
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作者：Fu, Baohua; Hwang, Jun-Muk
作者单位：Korea Institute for Advanced Study (KIAS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：The prolongation of a linear Lie algebra plays an important role in the study of symmetries of G-structures. Cartan and Kobayashi-Nagano have given a complete classification of irreducible linear Lie algebras with non-zero prolongations. If is the Lie algebra of infinitesimal linear automorphisms of a projective variety SaS,a(TM) V, its prolongation is related to the symmetries of cone structures, an important example of which is the variety of minimal rational tangents in the study of unirule...
