Abstract:In this talk, we first introduce various models to study what a generic 3-manifold looks like. We then focus on the Heegaard splitting model of 3-manifolds, equipped with geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a generic Heegaard splitting goes linearly to the infinity. In particular, generic 3-manifolds are hyperbolic in this mode...
Abstract:For a smooth projective variety X over C , the global sections of the symmetric algebra of the tangent bundle form a C-algebra S(X) , which has been little studied up to now. I will use a series of examples to show that this algebra is both interesting and difficult to calculate. I'll end with a theorem that bounds its (Krull) dimension in terms of the Kodaira dimension of X . This is ...