華東師范大學(xué)數(shù)學(xué)研究所建所10周年大會(huì)-文庫(kù)吧
2025-07-11 12:40 本頁(yè)面
【正文】 s theorem over Artinian subschemes.Sid Webster (University of Chicago)Title: Complete Integrability in Several Complex VariablesWe look for an analogue of the plete integrability of the geodesic flow on the ellipsoid in real Euclidean space. For CR geometry, this turns out to be the flow of certain characteristic vector fields on the real ellipsoid in plex space. We describe the relevant constructions.Ngaiming Mok (莫毅明，Hong Kong University)Title: Reconstructing certain rational homogeneous manifolds from minimal rational tangents In a joint programme of research with JunMuk Hwang of KIAS, Korea, we have been studying the geometry of uniruled projective manifolds by examining their varieties of minimal rational tangents. A natural question in this programme is the question of reconstruction, viz., to reconstruct a projective uniruled manifold X from its varieties of minimal rational tangents. Recently, we solved the problem in the case when X is a rational homogeneous manifold of Picard number 1 associated to a long simple root. An especially simple case of this result was developed earlier on and used by the author to study projective uniruled manifolds with nef tangent bundle, in relation a conjecture of CampanaPeternell39。s. Combined with a recent result of Hwang39。s we can now characterize projective uniruled manifolds with nef tangent bundle of Picard number 1 in a special case, viz., under the assumption that varieties of minimal rational tangents are 1dimensional at a general point.Xiangyu Zhou (周向宇, Chinese Academy of Sciences)Title: Group actions in several plex variables Stephen S T Yau (丘成棟，ECNU, University of Illinois at Chicago)Title: Global invariants for strongly pseudoconvex varieties with isolated singularities: Berrgman functionsLet M be a strongly pseudoconvex manifold which is a resolution of strongly peudoconvex variety V with only isolated singularities. We define a Bergman function BM on M which is a biholomorphic invariant of M. The Bergman function BM vanishes precisely on the exceptional set of M. Hence B_M can be pushed down and we obtain a Bergman function BV which is a biholomorphic invariant of V. The Bergman function not only can distinguish analytic structures of isolated singularities, but it can also distinguish the CR structures of the boundaries of V. As an application, we define a continuous numerical invariant on strongly pseudoconvex CR manifolds in V={(x,y,z): xy=z2}. We show that our invariant varies continuously in R when the CR structure of strongly pseudoconvex manifold changes in V. Moreover we show that the Bergman function allows us to determine the automorphism groups of these CR manifolds. Xiaojun Huang (Rutgers University)Title: A simultaneous embedding problem for a CR family of CR manifoldsSongYing Li (University of California, Irvine)Title: Boundary value problem of plex MongeAmpere equations Ben Chow (University of California, San Diego)Title: Collapsing sequences of solutions for Ricci flowKefeng Liu（劉克峰，UCLA）Title: Localization and string dualityI will discuss the proofs of conjectures arising from the duality conjecture between gauge theory and string theory, including the MarinoVafa conjecture, and recent progress on the GopakumarVafa conjecture. Several techniques of localizations are used on various moduli spaces in equivariant cohomology and Ktheory. Hourong Qin (秦厚榮，Nanjing University)Title: Rank of K2 of Elliptic
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