There will be an open competition for PhD positions in Mathematics in Italy (link). Selection procedures will be carried on this summer according to Italian National rules. Deadline for applications is April 30th. If selected, you will be able to choose directly our University as your host institution without any further procedure.
Let me give you briefly a few additional pieces of info.
The salary is about 1,000 euros per month, after taxes.
Since many years now INDAM (an Italian academic institution) funds grants for non EU foreign students enrolled in PhD courses. In the year 2007, four grants were awarded. Three are expected to be in 2008. Please find here the related announcement: in your application you must state a "declaration of intents" for applying to a specified Italian PhD course in mathematics at an Italian university (you may choose Dottorato in Matematica del Calcolo at Insubria U. - Como) within the end of the same year. A copy of the application to the Italian PhD course must be attached.
                                                                      Prof. Stefano Serra-Capizzano
 

FOR NON-ITALIAN CANDIDATES:
Application form (download)
Concerning your potential participation to the selection procedure (an interview November 8th, of more or less one hour, on your interest and expertise in Mathematics), here is some more precise information:
1) There are up to 5 positions without salary (people usually take such positions if they have already some kind of salary and/or support from other institutions); 2 of these are reserved to non-EU candidates. If any of you are interested in this kind of position, please contact the coordinator Serra Capizzano  (s.serracapizzano@uninsubria.it).
2) There are 3 positions with a salary of about 900 euros per month (after tax); one of them is on a specific theme i.e. Web Search Engines and/or Algorithms for Image/Signal reconstructions. The salary is not high but you can live in Como, also because we can help you in finding cheap accommodation.
3) For these positions (both of type 1) and 2)) you have to attend to the selection procedure, which will be in Como, Department of Physics and Mathematics, Via Valleggio 11, 22100 – Como (Italy). The date is November 8th, at 2 pm, Room 4.14 (4th floor) or Aula Magna (ground floor). 
4) To attend to the selection procedure it is necessary to pay 40 euros (forty euros) into the University Administration via Postal Account cc 1422621, Servizio Tesoreria, U. Insubria, via Ravasi 2, Varese. Since such a payment into a Postal Account could be non-trivial, we have decided that for foreign candidates it may be made once you arrive in Italy for the selection procedure (for instance, on November 8th in the morning).
5) Since traveling to Italy could be non-trivial, we decided to give the possibility of interviewing the foreign candidates by video-conference. In that case the 40 euros should be paid by bank transfer to the  Postal Account cc 1422621, Servizio Tesoreria, U. Insubria, via Ravasi 2, Varese, before the interview.
6) To attend to the selection procedure it is also necessary to fill in an Application form. Be careful in filling it in and in presenting the correct documents. You should then send the Application Form, properly filled in and signed, the requested documents, presentation letters, a detailed CV, and a list of your relevant scientific activities (honours, merits, school attended, conferences attended, abstracts, published papers etc.)  to: Magnifico Rettore, Univ. Insubria, Via Ravasi 2, 21100 Varese – Italy. Oggetto: Domanda Ammissione Dottorato in Matematica del Calcolo.
7) Since the translation in Italian of the Master Degree Certificate could be expensive and time consuming, we decided that it could be presented just before the formal beginning of the PhD activity (typically in late December or in January).