Infinite dimensional holomorphic homogeneous regular domains

In a collaboration with C.-H. Chu (London), S. Kim (Postech), I have shown that the infinite dimensional HHR(=holomorphic homogeneous regular) domains are domains of holomorphy, and determined completely which infinite dimensional bounded symmetric domains are HHR. This extends the study of HHR domains in the finite dimensional complex geometry. In this talk, I will report these results with (hopefully) comprehensive introduction of this direction of study, which is relatively new.