Past Seminars- Differential Geometry

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  • Jonathan Zhu
    Tue Jan 16, 2018
    4:00 pm
    We describe the construction of closed constant mean curvature (CMC) hypersurfaces using min-max methods. In particular, our theory allows us to show the existence of closed CMC hypersurfaces of any prescribed mean curvature in any closed Riemannian manifold. This work is joint with Xin Zhou.
  • Greg Pearlstein
    Tue Dec 5, 2017
    4:00 pm
    I will give an overview of recent work with P. Brosnan on the asymptotic behavior of archimedean heights, and with C. Peters on the differential geometry of mixed period domains.
  • Sheel Ganatra
    Tue Nov 28, 2017
    4:00 pm
    We introduce a new class of non-compact symplectic manifolds called Liouville sectors and show they have well-behaved, covariantly functorial Fukaya categories.  Stein manifolds frequently admit coverings by Liouville sectors, which can be used to understand the Fukaya category of the total space (we will study this geometry in examples). Our...
  • Qi Zhang
    Tue Nov 21, 2017
    4:00 pm
    Consider the scaling invariant, sharp log entropy (functional) introduced by Weissler on noncompact manifolds with nonnegative Ricci curvature. It can also be regarded as a sharpened version of Perelman's W entropy  in the stationary case. We prove that it has a minimizer if and only if the manifold is isometric to $\R^n$. Using this...
  • Rui Wang
    Tue Nov 7, 2017
    4:00 pm
    In this talk, I will first review our work on defining a new quantum deformation for the (Chen-Ruan) cohomology ring of a symplectic reduction. Then I will explain the relation between this quantum deformation and the well-known quantum cohomology ring. Our construction is based on the study of moduli spaces of symplectic vortices with proper...
  • Yu-Shen Lin
    Mon Oct 30, 2017
    4:00 pm
    We will start from the motivation of the tropical geometry. Then we will explain how to use Lagrangian Floer theory to establish the correspondence between the weighted counting of tropical curves to the counting of holomorphic discs in K3 surfaces. In particular, the result provides the existence of new holomorphic discs which do not...
  • Bogdan Suceava
    Tue Oct 17, 2017
    4:00 pm
    In 1934, Wilhelm Blaschke’s attention focused on a recent construction in metric geometry proposed by Dan Barbilian as a generalization of various models of hyperbolic geometry. It was the year when S.-S. Chern started his doctoral program under Blaschke’s supervision in Hamburg and when in several academic centers in Europe scholars...