Do graduate programs concentrated on complex analysis exist? I’ve been searching for a graduate university program which would concentrate on complex analysis in several variables, but wasn’t very successful. A mathematician friend of mine told me that complex analysis is currently not developed very actively, and is kind of not "fashionable". 

Is this true, and is there not so much to develop anymore? I know there are some open problems in Complex Analysis, but I'm concerned that there appears to be lack of interest in this field in academia in general. Are there specific good reasons for this lack of interest?
Actually, check out CUNY Grad Center.  iirc, lots of faculty at CUNY list complex analysis as one of their research areas.