In this seminar, Professor Chen Jiang started with several basic notions like geometric genus and canonical volume in birtaional geometry and introduced the question of geography problem. On algebraic surfaces, the boundary of geography problem is given by Miyaoka-Yau inequality and Noether inequality. Then he explained generalizations of the story on 3-folds, including his joint work with M. Chen and J.K.Chen. Finally he gave an outline for the proof of his main theorem.

Reported by Yalong Cao