Kahler-Einstein metric, K-stability and K-moduli spaces

Kahler-Einstein metric, K-stability and K-moduli spaces

Chenyang Xu, Princeton University
Fine Hall 314

In-Person and Online Talk

Zoom link:  https://princeton.zoom.us/j/99136657600

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Kahler-Einstein metric is a vast generalization to higher dimension of the canonical metrics on compact Riemann surfaces. Investigating it, called the Kahler-Einstein problem, on complex varieties with positive first Chern class (such varieties are named after Fano) has been a central theme in complex geometry for more than three decades. In recent years, people have built up a purely algebraic theory which is the key to complete the solution of the singular Kahler-Einstein problem, as well as fulfill the long term fantasy in higher dimensional geometry of constructing a moduli space for (many) Fano varieties. I will outline some of the main ideas in the development of this new theory.