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

自2011年以来，圣母大学数学中心一直在组织和举办各种数学主题的年度暑期课程。该中心的目标有两个方面：第一，为本科生和研究生提供必要的数学背景知识，使他们能够理解和欣赏数学研究的最新发展。这是通过由主要研究人员讲授的一系列迷你课程来实现的，这些研究人员的讲课目标是达到适当的水平。第二个目标是通过在项目的最后一周举办一次会议，广泛传播这些领域的最新进展。该中心还寻求通过积极招募代表性不足的群体参加活动来增加数学工作人员的多样性。这项资助将支持中心未来三个夏季计划的项目。该计划在2014年将致力于非线性偏微分方程在几何和物理。许多物理原理都是一个潜在变分原理的表达；同时，物理定律通常有一个纯粹的几何描述。几何和物理中的非线性偏微分方程项目的目标是将研究偏微分方程的研究人员与微分几何和数学物理联系在一起。2015年的课程将专注于边界和动态。近年来，许多问题和技术都利用了群作用在无穷远处物体上的统计性质。边界和动力学计划的目标是探索涉及几何和遍历理论中的边界概念的主题。2016年的计划将致力于广义稳定性，伪有限组合学和相关主题。在过去的几年里，模型论、组合学、李群、数论和动力学的思想也有了显著的融合。“广义稳定性、伪有限组合学及相关课题”课程的主要目标是促进在这些相关领域工作的数学家之间的互动。

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.