Metro Area Differential Geometry Seminar




Directions & Local

Past Meetings


The following speakers are confirmed:

  • Robert Bryant (Duke University)
  • Title: Curvature-Homogenous Metrics in Dimension 3

    A Riemannian manifold $(M,g)$ is said to be Curvature-homogeneous if it is homogeneous to second order, i.e., if, for any two points in $M$ the Riemannian tensors are equivalent under some isometry of the two tangent spaces. Of course, a locally homogeneous metric is curvature-homogeneous, but the converse is not true in dimensions greater than $2$. ( For a surface (i.e in dimension $2$) curvature-homogeneity is equivalent to having constant Gaussian curvature, and such metrics are, of course, all classified locally and they are locally homogeneous.) Already in dimension $3$, there are many questions about the existence and generality of curvature homogeneous metrics, even locally. In this case, curvature-homogeneity is equivalent to having the eigenvalues of the Ricci curvature be constant, which is a system of partial differential equations on the metrics.

    In the talk, I will review what is known about such metrics in dimension $3$, particularly the work of O.Kowalski and his collaborators during the 1990s. I will show that, for certain values of the eigenvalues of the Ricci tensor, these partial differential equations are integrable by the Darboux' method, which yields some surprising relations with classical subjects, such as the theory of holomorphic curves in the complex projective plane.

  • Karsten Grove (University of Notre Dame)
  • Title: Special Symmetry Groups in Non-Negative Curvature

    All explicitly known examples of manifolds with positive or nonnegative curvature have come about via constructions involving symmetry. In this talk we will confine our discussion to so-called polar actions (actions with a section) and actions by reflection groups. We will present strong classification and structure theorems in this context.

  • Gang Tian (Princeton University)
  • Title: K-stability implies CM-stability

    Both K-stability and CM-stability were first introduced on Fano manifolds in 90s and generalized to any polarized projective manifolds. In this talk, I will show how the K-stable implies CM-stable. I will also discuss their relation to Geometric Invariant Theory and the problem on existence of constant scalar curvature Kahler metrics.

    Past Speakers

    Spring 2015 (at JHU).
    Fall 2014 (at UMD).

    Updated Fall 2015 -- Department of Mathematics, Johns Hopkins University. Please contact Jacob Bernstein about errors on this site.