In weighted Kähler geometry, we consider Kähler manifolds equipped with a torus action and a fixed positive function on the moment polytope.  I will introduce this setting, as well as the notions of canonical metrics in weighted Kähler geometry: weighted solitons and weighted cscK metrics.  I will then review some results on existence of such metrics, and applications to the more classical Kähler-Einstein metrics, Kähler-Ricci solitons and Calabi's extremal Kähler metrics.

Zoom link:  texastech.zoom.us/j/93346469342