This NSF award supports the "Conference on integrable systems, random matrix theory, and combinatorics", which will take place at the University of Arizona, October 23-27, 2013. The goal of the conference is to foster interaction between researchers in integrable partial differential equations and researchers working in random matrix theory and combinatorics. The event is timely because integrable methods are now ready to have an impact on problems of graphical enumeration and newly discovered combinatorial identities make the rigorous proof of the full expansion of partition functions a reachable goal. The conference will include morning lectures on the most recent developments in random matrix theory and integrable systems, followed by afternoon workshops to investigate new research directions and collaborations in these areas. The majority of the participants will consist of junior researchers and graduate students. Information about the conference can be found at the conference website http://math.arizona.edu/mcl/CombConf.htm.
The main objective of the conference is to promote research and education in the areas of partial differential equations and random matrix theory and combinatorics, and to bring together senior researchers, junior researchers and graduate students from two exciting active areas in mathematics with potential applications to mathematical biology and theoretical physics.
on the campus of the University of Arizona, Tucson, Arizona. The conference ran from October 23 to October 26, 2013. There were at least 41 full conference participants. Funding from the NSF was used to support the attendance of 18 students, 5 young researchers, and 18 senior researchers. Of participants funded, 16 were female or minorities. The conference featured a unique program with research presentations in the morning followed by breakout working groups in the afternoon. There were a total of fifteen presentations, in addition the conference organizers coordinated with the Department of Mathematics so that the regularly scheduled Mathematics Colloquium on October 24 by Maciej Zworski, and the Applied Mathematics Colloquium on October 25 by Peter Miller were included in the conference program. Proposals for the working groups were collected from Senior and Young researchers ahead of the conference and were posted on the conference wiki http://ercolani60.wikidot. com. Working groups were encouraged to use the wiki to collaborate and collect notes and results from their sessions. There were a total of four working groups that ran (we divided participating students up among the working groups and encouraged researchers to participate): Universal Wave Patterns in Integrable Nonlinear Waves with Robert Buckingham and Peter Miller; Codes, Modes, Nodes and Roads with Nicholas Ercolani; Curve Flows and Soliton Equations with Analisa Calini; Nonlinear models in DNA dynamics with Jesu ?s Adria ?n Esp ??nola-Rocha. The impact of the activity included: Participation of women, minorities, young researchers and students. One goal of the activity was to expose graduate students to a problem adjacent to the ones on which they are focusing as students. The working group activity in the afternoons provided a chance for students to work deeply into a problem, a different experience from a normal conference presentation. A variety of talks in nonlinear waves and integrable systems. NSF money supported the travel, particularly of young researchers and students to the conference. Further funds provided by the Department of Mathematics at the University of Arizona supported the conference facilities, refreshments and incidental expenses. Remaining funds were used in July 2014 to support the continued effort of the working groups. The group working on Universal Wave Patterns met at the University of Michigan to continue their project. This group has maintained contact and continued working beyond the initial collaboration started at the conference in October 2013, includes the participation of women and students in the collaboration. The topics for lectures at the conference ranged over Integrable Nonlinear Partial Differential Equations, Random Matrix Theory, and Combinatorics. Four working groups ran, and generated great synergistic activities during the afternoons. These working groups did not end with the conference. Two of them (Universal Wave Patterns in Integrable Nonlinear Waves, and Codes, Modes, Nodes, and Roads) continued after the conference and have turned into active research projects. The conference funding was used to support a research visit at the University of Michigan, for conference participants Robert Buckingham, Megan McCormick, and David Smith (where they continued work on Nonlinear Waves with Peter Miller). Although that project has taken on a life of its own (and is out of our immediate control), we have learned that there will be a new conference / working group proposal from their group.