Speakers
 The following speakers are confirmed:
 Matt Gursky (Notre Dame)
 Title: Gap and index estimates for some conformally invariant problems in 2 and 4d.
 Abstract:
In this talk I want to discuss sharp 'gap' estimates for the energy of YangMills connections in 4d, and the related question of the energy of harmonic twospheres. I will also talk about index estimates for YangMills connections and Einstein metrics in 4d.
 Joel Spruck (JHU)
 Title: Total Curvature and the isoperimetric inequality in negatively curved manifolds
 Abstract:
We prove that the total positive GaussKronecker 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 CartanHadamard 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
 Abstract:
Notions of noncollapsing 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.
