Abstract:

Over the past 40 years, gluing constructions have become ubiquitous in geometric analysis, giving us new examples of compact manifolds with holonomy G_2 (Joyce), constant mean curvature surfaces (Kapouleas), and more recently, novel translating solutions to Lagrangian mean curvature flow (Su). In this talk, I hope to give an accessible overview of the philosophy of gluing constructions, through the example of finding Calabi-Yau metrics on the K3 surface. The talk will mainly follow the expository article 'Calabi-Yau Metrics on the K3 Surface as a Model Gluing Problem' by Donaldson.