I do not offer any PhD. Thesis topics via the SIS: it is too individual and I want to talk to the candidate first. In particular, to start a PhD research in proof complexity or, more generally, on a topic connecting mathematical logic and computational complexity, you ought to have a solid background in both these areas. I also expect that the candidate's MSc. thesis or some other work clearly demonstrates his or her ability for an independent research work.
Some information about the PhD program and, in particular, about the admission procedure is at the University page and at the Faculty page. See also for further relevant info. There are various stipend schemes, some permanent and some ad hoc based on grants, to help with your expenses.