I will discuss the recent work with Gang Liu on the diameter rigidity for Kahler manifolds with positive bisectional curvature.

The Fargues-Fontaine curve is a fundamental object in p-adic Hodge theory. I will mention some of the important properties of the curve, then introduce the rings that are used to build the curve. These are the extended Robba rings; they share many properties with the one dimensional affinoid algebras of rigid analytic geometry. I will discuss these similarities, point out some key differences, and explain how to adapt some proofs from rigid geometry to bypass these differences. The pre-talk will give an overview of some of the basics of rigid analytic geometry.