Department of Mathematics - Mathematics Colloquium - On extremal Kaehler metrics

This is an expository lecture on Kähler geometry, in particular, on extremal Kaehler metrics. In 1950s, E. Calabi propose an ambitious program on the existence and uniqueness of extremal Kaehler metrics. For more than 70 years, Calabi's program attract generations of Kaehler geometers to work on. This is an area in which I have privilege to be involved where my own research has been greatly shaped by Calabi's vision directly. This lecture is expository, starting with my thesis, up to the latest work with my young collaborators on extremal Kaehler metrics.