I work in a Department of Mathematics in the Irish Institute of Technology sector. 

Funding for mathematics research has been reduced by the Higher Education Authority and between this, a heavy teaching load and other reasons, staff are either not very active or completely inactive in research. There are a number of departments who are very active in their research.

I am interested in exploring the idea of setting up a problem session in the institute where the research community would be invited to present problems they are having in their research that they feel mathematics department staff might be able to shed light on.

At the moment questions I have include:

* has this been done in other institutions?
* if yes, has it been beneficial to both communities?
* will researchers share their problems; will the sessions sustain themselves?
* how regularly should such a problem session take place?
* should problems be presented at the session and solved in the next session or presented prior to the session?

I feel there are a number of obvious benefits that could come from such an endeavour and I am looking for help in seeing potential problems, etc.

I hope this question, although quite open-ended, is appropriate for this site.

**Edit:** Regarding the comments below

Thank you all for your help. These sessions would be primarily focussed on staff in the institute and incubated industry. I wouldn't envisage them being of the duration of a workshop: rather just a single afternoons. I am looking at something a lot less formal than the workshops ye survive. I have heard of the ESGI thank you Ruadhaí.