Center for Mathematics at Notre Dame, June 2-6, 2014

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Since 2011, the Center for Mathematics at the University of Notre Dame has been organizing and hosting annual summer programs on various mathematical themes. The goal of the Center is two-fold: first, to provide students at the undergraduate and graduate level with the necessary mathematical background so they can understand and appreciate recent developments in mathematical research. This is accomplished through a series of mini-courses taught by leading researchers, who aim their lectures at the appropriate level. The second goal is to broadly disseminate current advances in these areas by hosting a conference in the final week of the program. The Center also seeks to increase the diversity of the mathematical work force by actively recruiting underrepresented groups to attend the activities. This grant supports the programs planned at the Center for the next three summers.The program in 2014 will be dedicated to Nonlinear PDEs in Geometry and Physics. Many physical principles are an expression of an underlying variational principle; at the same time, physical laws often have a purely geometric description. The goal of the Program in Nonlinear PDEs in Geometry and Physics is to bring together researchers who are working on PDEs with connections to differential geometry and mathematical physics. The program in 2015 will be dedicated to Boundaries and Dynamics. In recent years a number of problems and techniques have used statistical properties of a group action on an object at infinity which can be considered as a boundary. The goal of the Program on Boundaries and Dynamics is to explore themes involving a notion of boundaries in geometry and ergodic theory. The program in 2016 will be dedicated to Generalized Stability, Pseudo-finite Combinatorics and Related Topics. The last few years have also seen a remarkable convergence of ideas in model theory, combinatorics, Lie groups, number theory, and dynamics. The main goal of the Program on Generalized Stability, Pseudo-finite Combinatorics and Related Topics is to facilitate interactions between mathematicians working in these related areas.