I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the presentation to be geared towards applying the material we've learned to concepts in physics.
We've learned about Kahler manifolds and their properties, and have spent a bunch of time learning about PDEs. Topics have included Sobolev inequalities, elliptic regularity, Schauder theory and other elliptic PDE stuff. We are also studying the Calabi-Yau theorem.
Any topic suggestions and reference requests are appreciated.