Speaker: Naoto Yotsutani(University of China Science and Technology)

Venue: 82J04, BICMR

Time: October 23, Wednesday, 10:10am --12:00am

Abstract: This is the survey talk on (semi)stability notions in Kahler and algebraic geometry defined by S.Paul (Annals of Math.(175),2012,arXiv:1308.4377) very recently. The fundamental motivation to consider this new perspective of stability relates the "standard conjecture"--necessary and sufficient conditions for the existence of "canonical" Kahler metrics. Paul's crucial point of view is to generalize the Kempf-Ness theorem in (finite dimensional) Geometric Invariant Theory in order to capture the asymptotic behavior of K-energy map. In the first half of our discussion, we will quick review on the classical GIT and will see how to describe the set of semistable points by using the Hilbert-Mumford criterion.

Later on, we will likely to develop our argument for dealing with the K-energy map in Kahler geometry analogous to the Kempf-Ness function in the classical GIT. It is the aim of this talk to share our understandings on the recent progress of these topics.