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.