For over 50 years, the International Mathematical Olympiad (IMO) has
stimulated pre-college students to pursue their talents in Science,
Technology, Engineering, and Mathematics.  In the United States, it
furnishes the context for the Mathematical Olympiad Summer Program (MOSP),
which brings together the top 60 students identified by the national
selection competition.  This training camp has historically provided
high-level enrichment and guidance to these potential future leaders, and
it is structured as an intensive 3-week training camp in which students
engage in mathematical activities from day to night.

This award supported two new initiatives which leverage the existing
Olympiad infrastructure.  The first used the new female-targeted editions
of the IMO (the China Girls' Math Olympiad, a multinational competition
organized by China, and the European Girls' Math Olympiad) as context to
substantially increase the participation of women at the highest levels of
the United States Olympiad program.  Over the grant period, 10 girls were
invited to the Math Olympiad Summer Program each year, where they developed
their mathematical breadth and depth, and built a strong network.  The
international events further expanded their network to global-scale.

The second initiative added a research dimension to MOSP by taking
advantage of its pool of faculty and alumni, many of whom have moved into
professional research careers.  The MOSP staff roster includes
representatives from every career stage, from first-year undergraduate to
tenured professor.  This award effectively broadened the scope of the
program, as instructors made efforts to link instruction with research, and
to incubate interdisciplinary collaborations within the MOSP faculty
itself.  An evening seminar was introduced into the MOSP routine, running
from 7-8pm on alternate nights.  The speakers were MOSP instructional staff
who had gone on to graduate school and beyond.  The mission was to convey
the spirit of each speaker's current area of investigation, in terms which
were comprehensible to the high-school students.

The highlight was a new system, which was piloted for a segment of the
instructional staff, loosely based on the successful model of the modern
research university.  In this new approach, the PI and other senior
instructional staff had the explicit objective of mentoring the junior
staff on research projects, in addition to teaching courses to the
high-school students.  Many of the research collaborations were
intentionally conducted in public (over a wide variety of hours), in a
large common lounge where students typically congregated to relax.  This
inspired numerous inquiries from the students, who then learned not only
about the problems at hand, but also about the research process.

Each summer had an average of 4 research collaborations involving
undergraduates, spanning topics as diverse as representation theory,
combinatorics, economics, and theoretical computer science.  Many of them
produced substantial progress.  In two cases, the results reached the level
of mainstream peer-reviewed scientific journals or conferences, and those
two papers have been accepted for publication.  In both projects, the
undergraduate research assistants made core contributions.  As a result,
several talks were given on these two projects at conferences and seminars
across the country, by the PI and by the student co-authors.  A number of
the other investigations are still on-going.

In conclusion, this pilot has demonstrated the proof of concept for a new
platform, which brings together talented high-school students in a
vertically-integrated research and learning environment.  The Math Olympiad
Summer Program will now permanently switch over to this model, which melds
a high-school enrichment camp, an REU, and an inter-disciplinary research
workshop into a coherent, symbiotic entity.
                    

                
                

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