MAT 644 Topics in Differential Geometry

Gluing Constructions of Canonical Metrics

Fall 2018

SUNY at Stony Brook

The construction of solutions of geometric structures and geometric PDE on manifolds is now pervasive in numerous areas of geometry. The most famous and still ideal example is Taubes' construction of self-dual Yang-Mills instantons. This course will be a tour through various instances of the gluing technique, mainly restricted to geometric problems involving Riemannian metrics, especially Einstein metrics.

A selected list of papers on this topic is here

The grade for the class will be based on class participation and/or lecture presentation.