What math institutes offer research in pairs/research in teams? Some math institutes offer programs in which a small number of researchers are enabled to meet at the institute for a week or more.  A list seemed as if it could be useful. 
 A: RIMS Kyoto says (in Japanese) they host at least two for 1-2 weeks collaboration http://www.kurims.kyoto-u.ac.jp/ja/research-01.html
A: There is also a Research in Pairs program at the ICMAT, in Madrid. From the institute page, 
Research in pairs Programme aims at small groups of 2-4 researchers from different places working together on a specific project for a short period of time.
A: The Mittag-Leffler institute near Stockholm has another RIP (this time it stands for "Research in peace") programme.
A: This program is fairly new, but I can say from experience that it's a beautiful facility and great working environment.
Collaborate@ICERM
https://icerm.brown.edu/collaborate/
Collaborate@ICERM offers teams of 3-6 researchers the opportunity to spend five days at the institute during the summer (May-August) or in the month of January. The team research project should have a computational or experimental component. 
A: The Centro di Ricerca Matematica Ennio De Giorgi at the Scuola Normale Superiore of Pisa usually has a program of research in pairs: 
http://crm.sns.it/visit/pairs.html
A: The International Centre for Mathematical Sciences (ICMS) in Edinburgh (Scotland) offers Research in Groups.  This institute is associated to the University of Edinburgh and Heriot-Watt University.
There’s more information on the linked page, but the gist of it is this:


*

*2-4 researchers wishing to organise a short, intensive period of research in Edinburgh

*at least one researcher must be based in the UK

*not all researchers should be from the same university, with a maximum of two researchers from any one university


There are three deadlines for submitting a Research-in-Groups proposal each year: 30 April, 30 August and 30 December.
A: The CIRM in Trento (Italy) has a Research in pairs program (for 2-3 people, 1-6 weeks):
http://cirm.fbk.eu/research-pairs
A: The Erwin Schrodinger Institute in Vienna has a research in teams program:
https://www.esi.ac.at/activities/research-in-teams-short
Unlike some other programs, this supports visits of 1 - 4 months.
A: As far as I know, the "Research in Pairs" program appeared first and still exists in the Mathematisches Forschungsinstitut Oberwolfach. See http://www.mfo.de/
As for the list of such possibilities, one can look through the list of all institutes of this kind:
http://www.math.psu.edu/MathLists/institutes.php 
A: BIRS in Banff, Alberta, Canada, offers "research in teams" (2-4 people, 1-2 weeks) and "focussed research groups" (up to eight researchers, 1-2 weeks).
A: In France:
a. Institut Henri Poincaré (Paris)
'Research in Paris' (yes, Paris not pairs) 
http://www.ihp.fr/en  (under "Activities" one will find "Research in Paris")
b. CIRM (Marseille/Luminy)
'Recherche en binôme' / Research in pairs
http://www.cirm-math.com/ (under "Scientific"  one will find "research in pairs")
A: The Hausdorff Institute in Bonn (http://www.hausdorff-research-institute.uni-bonn.de/index) offer research in small groups of size at least 3.
A: The American Institute of Mathematics in San Jose has a nice program for collaborations:
http://aimath.org/research/squares.html
A: This is a little bit off the beaten path, and definitely not for all personalities, but the high school summer program Canada/USA Mathcamp has a Research in Pairs program (details here) for which we're happy to receive unsolicited applications.  In brief: collaborators visit the program, teach 1 hr/day (on whatever they'd like) to very very bright high school students, and spend the rest of their time on their research program.
A: As of today, an additional option exists at EPFL:
https://bernoulli.epfl.ch/bernoulliBrainstorm
