華東師范大學(xué)數(shù)學(xué)研究所建所10周年大會-資料下載頁
2025-07-26 12:40本頁面
【正文】 aphs is hamiltonian, the Veldman conjecture that if a simple 3connected crawfree graph G on n vertices with minimum degree at least (n+5)/10, then either G is hamiltonian, or the minimum degree of G is exactly (n+5)/10 which can be constructed from the Petersen graphs. We will also discuss the latest progresses made on the relaxation of local connectedness of crawfree graphs and on the ThomassenMathews conjecture that every 4connected crawfree graph is hamiltonian.Bei Hu (胡鋇，University of Notre Dame)Title: The location of initiation of angiogenesis of a 1dimensional blood vesselAngiogenesis is a process of sprouting of new blood vessels from preexisting vascular network. This process occurs during placental growth, during wound healing, and in tumor growth. In the latter it is initiated by release of chemicals by the tumor, the so called ``tumor angiogenic factor39。39。.In tumor growth, tumor releases chemotactic substances, this chemical bine with the receptors on the endothelial cell wall, this process produce substances which cause the eventual sprouting lining of new capillaries. We want study the stability of such a system, and find the conditions for a global attractor, which may predict the location of the initiation of angiogenesis.Jiaping Wang (王嘉平，University of Minnesota)Title: Kahler manifolds with positive spectrumIn this talk, we will explain some joint work with Peter Li on the topology of plete Kahler manifolds with positive spectrum. Under suitable bisectional curvature lower bound, we show such manifolds must have only one infinite volume end. Furthermore, for Kahler surfaces, we can also show the number of cusps must be finite.XiNan Ma (麻希南, East China Normal University)Title: The convexity of solutions of elliptic PDE and its applications to classical differential geometryWe first review the history of convexity of solutions of elliptic PDE, then we concentrate on the deformation technique for the fully nonlinear elliptic PDE. At last we give some applications to geometry problems from convex body. HongWen Lu (陸洪文，Tongji University)Title: On Pellian Equation ConjecturesIn the talk, I will disscuss Pellian equation, which is related with AnkeyArtinChowla’s conjecture and Mordell’s conjecture.Huaxin Lin (林華新，ECNU, University of Oregon)Title: Classification of amenable C*algebrasC*algebra theory is often regarded as nonmutative topology. This talk is to give a brief report on the program of classification separable amenable C*algebras. We will show Ktheory can be used to give a classification theorem (up to isomorphism) for certain amenable separable simple C*algebras. This is of course very different from the mutative case. We will mention E. Kirchber and N. C. Phillips39。s result on purely infinite simple C*algebras and G. Gong and G. A. Elliott39。s result on simple AHalgebras. The main topic will be the recent result on separable amenable simple C*algebras with lower rank. Applications to topological dynamics will also given. Shengli Tan (談勝利, East China Normal University)Title: Applications of stability of vector bundles and algebraic invariant theoryWe are going to present the recent geometric applications of Bogomolov’s inequality between the Chern numbers of a semistable vector bundle. We shall also explain why the stability method does not work for higher dimensional manifolds and what is the possible generalization from the point of view of algebraic invariant theory. 17
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