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作者：Caprace, PE; Mühlherr, B
作者单位：Universite Libre de Bruxelles
摘要：We give the solution of the isomorphism problem for Kac-Moody groups over algebraically closed fields of any characteristic. In particular, we prove a conjecture of Kac and Peterson and compute the automorphism group of a Kac-Moody group over an algebraically closed field of characteristic zero.
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作者：Welschinger, JY
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We first build the moduli spaces of real rational pseudo-holomorphic curves in a given real symplectic 4-manifold. Then, following the approach of Gromov and Witten [3,19,11], we define invariants under deformation of real symplectic 4-manifolds. These invariants provide lower bounds for the number of real rational J-holomorphic curves which realize a given homology class and pass through a given real configuration of points.
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作者：Birman, JS; Menasco, WW
作者单位：Columbia University; State University of New York (SUNY) System; Buffalo State University
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作者：Nakajima, H; Yoshioka, K
作者单位：Kyoto University; Kobe University
摘要：We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on R-4 gives a deformation of the Seiberg-Witten prepotential for N = 2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of R-4, we derive a differential equation for the Nekrasov's partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky...
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作者：Downarowicz, T; Newhouse, S
作者单位：Wroclaw University of Science & Technology; Michigan State University
摘要：Let f : X --> X be a homeomorphism of the compact metric space X. A symbolic extension of ( f, X) is a subshift on a finite alphabet ( g, Y) which has f as a topological factor. We show that a generic C-1 nonhyperbolic (i.e., non-Anosov) area preserving diffeomorphism of a compact surface has no symbolic extensions. For r > 1, we exhibit a residual subset R of an open set U of C-r diffeomorphisms of a compact surface such that if f is an element of R, then any possible symbolic extension has t...
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作者：Tian, G; Viaclovsky, J
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kahler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results were obtained for Einstein metrics in [And89], [BKN89], [Tia90], but our analysis differs from the Einstein case in that (1) we consider more generally a fourth order system in the metric, and (2) we do not assume an...
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作者：Ito, T
作者单位：Kyoto University
摘要：The aim of this paper is to prove the weight-monodromy conjecture (Deligne's conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply a positivity argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink. As an application, by combining our results with the results of Schneider-Stuhler, we...
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作者：Duan, HB
作者单位：Chinese Academy of Sciences
摘要：Let G be a compact connected Lie group and let H be the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resolutions of Schubert varieties and the enumerative formula on a twisted product of 2 spheres obtained in [Du(2)], we obtain an explicit formula for multiplying Schubert classes in the flag manifold G / H.
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作者：Mabuchi, T
作者单位：University of Osaka
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作者：Lee, JR; Naor, A
作者单位：University of California System; University of California Berkeley; Microsoft
