Thursday, September 13, 2018
Time  Items 

All day 

4:00pm 
09/13/2018  4:00pm We show that every 3uniform hypergraph with every vertex being contained in at least 5/9+o(1) proportion of all possible edges contains a (tight) Hamiltonian cycle. Several different lower bound constructions show that this degree condition is asymptotically optimal. Location:
DL 431
09/13/2018  4:15pm The volume of a hyperbolic 3manifold can be thought of as a measure of the “complexity” of the manifold. For hyperbolic manifolds of infinite volume instead of measuring the volume of the entire manifold one can instead take the volume of the “convex core” of the manifold which is typically finite. For infinite volume hyperbolic 3manifolds a single topological manifold will support a large deformation space of hyperbolic structures and the convex core volume is an important function on this space. Unfortunately, this function isn’t smooth (for the natural differentiable structure on the deformation space). KrasnovSchlenker have defined the notion of “renormalized volume” motivated by work of GrahamWitten on conformally compact Einstein manifolds. The renormalized volume is coarsely the same as the convex core volume but has the advantage that is it a smooth function and further KrasnovSchlenker have given a simple formula for its derivative. We will define this concept and then describe some of our joint work with J. Brock and M. Bridgeman studying its gradient flow. Location:
LOM 206
