A few doctoral positions are available. Ph.D. students receive a Ph.D. support contract of the Max Planck Society for three
years, based on the German TVöD 13 scale (75%). Extension to a 4th year is possible.
The Max Planck Institute will assist in finding housing (housing[at]mpim-bonn[dot]mpg[dot]de). All information about Visa/Residence permit Ph.D. students will obtain by the administration (personnel[at]mpim-bonn[dot]mpg[dot]de).
For a sketch of the approximate living expenses, have a look at some information provided by BIGS [2].
The IMPRS provides support for students to visit specialists in their fields at German or other European institutions with whom the IMPRS is connected.
There is also a limited budget for participation in conferences or workshops at these partner institutions, or for short invitations of specialists from these institutions to Bonn.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/46
[2] https://www.mathematics.uni-bonn.de/hsm-school/bigs/bigs#Practical