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作者：Alekseev, A; Meinrenken, E
作者单位：University of Geneva; University of Toronto
摘要：Let G be a connected Lie group, with Lie algebra g. In 1977, Duflo constructed a homomorphism of g-modules Duf : S( g). U( g), which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne ( 1978) proposed a conjecture on the Campbell-Hausdorff series, which ( among other things) extends the Duflo theorem to germs of biinvariant distributions on the Lie group G. The main results of the present paper are as follows. ( 1) Using a recent result of Torossian ( 2002), we establish t...
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作者：Shepherd-Barron, NI
作者单位：University of Cambridge
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作者：Sarnak, Peter; Strombergsson, Andreas
作者单位：Institute for Advanced Study - USA; Princeton University; Uppsala University
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作者：Axelsson, A; Keith, S; McIntosh, A
作者单位：Australian National University
摘要：We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge-Dirac operator on compact manifolds depend analytically on L-infinity changes in the metric. We also recover a unified proof of many results in the Calderon program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.
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作者：Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri
作者单位：Massachusetts Institute of Technology (MIT); University of Miami; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface X-k obtained by blowing up CP2 at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration W-k :M-k -> C with k+3 singular fibers, equipped with a suitable symplectic form. Moreover, we also show that this mirror correspondence between derived categories can be e...
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作者：Vaughan, R. C.; Velani, S.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of York - UK
摘要：The convergence theory for the set of simultaneously psi-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in [1] and thereby completes the general metric theory for planar curves.
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作者：Brubaker, Ben; Bump, Daniel; Friedberg, Solomon
作者单位：Stanford University; Boston College
摘要：To each reduced root system Phi of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Phi. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each...
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作者：Bhatwadekar, M.; Das, Mrinal Kanti; Mandal, Satya
作者单位：Tata Institute of Fundamental Research (TIFR); University of Kansas
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作者：Marinescu, G; Dinh, TC
作者单位：Humboldt University of Berlin; Universite Paris Saclay; Institute of Mathematics of the Romanian Academy; University of Bucharest; Romanian Academy
摘要：We show that the 'pseudoconcave holes' of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel's theorems to dimension two.
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作者：Phong, D. H.; Sturm, Jacob
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick; Rutgers University Newark
