During a Trimester Program, which lasts four months, the Institute invites a group of mathematicians or economists from all over the world to carry out research with a special emphasis on collaborative activities. The Institute can host up to 30 mathematicians at any one time and tries to distribute these places between senior mathematicians, postdocs and PhD students. The overall topic can come from all areas of mathematics, mathematical economy, and mathematical physics. During the programs one or the other workshop is organized as well as perhaps lecture series or schools. The stays are financially supported by the Institute.

The purpose of Dual Trimester Programs is to identify two research areas that have promising potential for cross fertilization and use this potential to foster innovation.

During a Junior Trimester Program, groups of excellent young scientists (PhD students, Post Docs, Junior Faculty within 6 years of their PhD completion),  carry out collaborative research. The participants can organize small workshops and can take the initiative to invite a senior mathematician with whom they can carry out research together. 

To enhance the long-term success of Trimester Programs, HIM offers the possibility to organize Follow-Up Workshops.These are held some time after the original Trimester Program, using the slots in between consecutive Trimester Programs.