- The following speakers are confirmed:
- Matt Gursky (Notre Dame)
- Title: Gap and index estimates for some conformally invariant problems in 2- and 4-d.
In this talk I want to discuss sharp 'gap' estimates for the energy of Yang-Mills connections in 4-d, and the related question of the energy of harmonic two-spheres. I will also talk about index estimates for Yang-Mills connections and Einstein metrics in 4-d.
- Joel Spruck (JHU)
- Title: Total Curvature and the isoperimetric inequality in negatively curved manifolds
We prove that the total positive Gauss-Kronecker curvature of any closed hypersurface embedded in a complete simply connected manifold of nonpositive curvature Mn, n ≥ 2, is bounded below by the volume of the unit sphere in Euclidean space Rn. This yields the optimal isoperimetric inequality for bounded regions of finite perimeter in M, and thus settles the Cartan-Hadamard conjecture. Our starting point is a comparison formula for total curvature of level sets in Riemannian manifolds. This is joint work with Mohammad Ghomi.
- Jonathan Zhu (Princeton)
- Title: Mean convex mean curvature flow with free boundary
Notions of non-collapsing for mean convex mean curvature flow have important consequences for the regularity and structure of such flows. We’ll discuss the generalisation of these results to the free boundary setting, including ongoing joint work with N. Edelen, R. Haslhofer and M. Ivaki.