Past Geometry and Analysis Seminar

4 November 2013
Joel Fine

I will explain a new formulation of Einstein’s equations in 4-dimensions using the language of gauge theory. This was also discovered independently, and with advances, by Kirill Krasnov. I will discuss the advantages and disadvantages of this new point of view over the traditional "Einstein-Hilbert" description of Einstein manifolds. In particular, it leads to natural "sphere conjectures" and also suggests ways to find new Einstein 4-manifolds. I will describe some first steps in these directions. Time permitting, I will explain how this set-up can also be seen via 6-dimensional symplectic topology and the additional benefits that brings.

  • Geometry and Analysis Seminar
27 May 2013
Martin Bridgeman

 Using thermodynamic formalism we introduce a notion of intersection for convex Anosov representations. We produce an Out-invariant Riemannian metric on the smooth points of the deformation  space of convex, irreducible representations of a word hyperbolic group G into SL(m,R) whose Zariski closure contains a generic element. In particular, we produce a mapping class group invariant Riemannian metric on Hitchin components which restricts to the Weil-Petersson metric on the Fuchsian locus. 
This is joint work with R. Canary, F. Labourie and A. Sambarino.

  • Geometry and Analysis Seminar