I welcome PhD students interested to do original research in the broad area connecting mathematical logic and computational complexity theory, and in proof complexity in particular.
I do not offer any PhD. Thesis topics via the SIS (the university Student Information Service): the choice of a suitable topic is too individual and I also want to talk to the candidate first. In particular, to start a PhD research you ought to have a solid background in both logic and complexity theory. 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 is no tuition fee and there are various stipend schemes, some permanent and some ad hoc based on grants, to help with your expenses. In particular, the Faculty has at present a stipend scheme in place that offers enough funds to be able to support yourself while studying in Prague.