Past Seminars- Differential Geometry

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  • Jiyuan Han
    Tue Sep 19, 2017
    4:00 pm
    Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with Jeff Viaclovsky.  
  • Julie Rowlett
    Tue Aug 8, 2017
    4:00 pm
  • Lucas Ambrozio
    Tue Jun 13, 2017
    4:00 pm
    We will review some recent work on free boundary minimal hypersurfaces. In particular, we will explain a geometric classification of the critical catenoid (joint with Ivaldo Nunes) and discuss what information about such hypersurfaces in a general ambient manifold one can extract from the knowledge of their Morse index (joint with Alessandro...
  • Bo Liu
    Tue Jun 6, 2017
    4:00 pm
    The eta form of Bismut–Cheeger is the higher degree version of the Atiyah-Patodi-Singer eta invariant, i.e. it is exactly the boundary correction term in the family index theorem for manifolds with boundary. In this talk, I'll study the properties of eta forms and extend them to the equivariant version for compact Lie group action....
  • Ke Zhu
    Mon Jun 5, 2017
    4:00 pm
    The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding....
  • Sebastien Picard
    Tue May 23, 2017
    4:00 pm
    The Lagrangian phase operator arises in the study of calibrated geometries and the deformed Hermitian-Yang-Mills equation in complex geometry. We study a local version of these geometric problems, and solve the Dirichlet problem for the Lagrangian phase operator with supercritical phase given the existence of a subsolution. They key step is to...
  • Steve Gindi
    Tue May 16, 2017
    4:00 pm
    Ever since the 1970's, holomorphic twistor spaces have been used to study the geometry and analysis of their base manifolds. In this talk, we will introduce integrable complex structures on twistor spaces fibered over complex manifolds that are equipped with certain geometrical data. The importance of these spaces will be shown to...