Dear Nathalie,
As far as I know, there is no list that includes all available PhD programs at Universität Hamburg.
The eight faculties of Universität Hamburg are in charge of the doctoral application and admissions procedure. Therefore, you can find all information regarding PhD program on the respective websites of the faculties. You will find the links here:
https://www.uni-hamburg.de/en/campuscen ... ml#2907515.
Information about the different procedural steps (e.g. application, admission, enrollment) can also be found on the website linked above.
Best wishes
Thomas Walter