Program:
Eight US students will be brought together with four Hungarian students to form two teams of six. Each team will have one Hungarian mathematician as an "advisor" and two US mathematicians as "mentors". The advisor and mentors for each team will work together to craft research activities that are appropriate to the team members' backgrounds and interests. The advisor is primarily responsible for guiding the overall themes tackled by the entire team, highlighting connections between insights made by team members, and suggesting new approaches and ideas when necessary. The mentors are primarily responsible for helping the students accomplish their day-to-day research activities, acting as a sounding board for the team members, and assisting the advisor in his/her advising role.

The program will be administered by two program directors. One of the directors will be from Hungary, and one of the directors will be from the US. The directors will be in residence during the summer program. The program would last for eight weeks during June and July, with an intense and short cultural immersion course that would precede the research portion of the program. Each of the advisors would be asked to invite two or three European mathematicians to give a weekly colloquium talk tailored for the program participants. The teams would also be asked to present their work to one another on a weekly basis.

The program directors and advisors would be chosen beforehand. The student and mentor positions, however, would be open and would be filled by the program directors with the assistance of the advisors. The size of the program is comparable to that of many current REUs, and the mix of Hungarian and US participants, advisors, and mentors would allow for substantial cross-cultural interactions. The advising structure is designed to allow US participants the opportunity to work closely with a Hungarian mathematician while not overwhelming him/her with many of the mechanics of being an REU advisor. The inclusion of Hungarian students in the program not only make this program stand out from the BSM set up, but it could also act as an incentive for the Hungarian mathematicians if it were made clear that they could each handpick two students from Hungary to work with them.

Expected Outcomes:
A successful program would have each of the student participants (including the Hungarian students if possible) presenting a poster at the Joint Meetings of the MAA, AMS and AWM in January of the following year. In addition, students would be encouraged to give talks at local MAA Section meetings and at Mathfest, the national MAA conference held in August. Students will also be encouraged to submit results to both undergraduate and standard peer-reviewed journals for publication.

In addition, a successful program will forge long term research connections between Hungarian and American mathematics faculty members. We anticipate that within the first 10 years of the program that one or more US faculty members would apply for Fulbright fellowships to spend a year conducting research in Budapest with the Hungarian faculty members they worked with as part of a summer research team. We would expect to see joint publications of US and Hungarian professors and also joint talks given at international conferences by the research teams of US and Hungarian professors.