Institute for Pure and Applied Mathematics

纯粹数学和应用数学研究所(IPAM)的使命是在广泛的数学家和科学家之间建立联系，开展新的合作，更好地向数学家和科学家提供关于跨学科问题的信息，并扩大数学的应用范围。这项提案的资金将通过将来自许多不同领域的研究人员聚集在一起为期1天至3个月的计划以及旨在教育和增加数学和科学多样性的活动来支持IPAM的使命。几乎每个项目都将数学和一个科学或工程领域结合在一起；大多数项目既包括纯数学，也包括应用数学；IPAM专注于重要的新兴主题，如蛋白质组学、互联网搜索引擎、压缩传感、纳米系统、虚拟手术和文档空间。在强调纯数学的项目中，IPAM致力于在致力于相关问题的不同研究小组之间建立联系。IPAM的研究计划通过促进不同数学领域之间以及数学与科学之间的互动来增强数学的活力；它们促进新的研究合作；它们帮助研究生、博士后和初级教师的职业发展；它们推动初级和高级科学家进入新的研究方向。其最终效果是建立新的科学社区，以应对我们这个时代复杂的科学挑战。IPAM的教育和多样性活动增加了学生进入科学工作队伍的人数，并鼓励妇女和代表性不足的少数群体充分参与数学和科学。这对于数学和科学在更广泛的社区中的生命力具有极其重要的意义。

The mission of the Institute for Pure and Applied Mathematics (IPAM) is to make connections between a broad spectrum of mathematicians and scientists, to launch new collaborations, to better inform mathematicians and scientists about interdisciplinary problems, and to broaden the range of applications in which mathematics is used. Funding from this proposal will support IPAM's mission through programs that bring together researchers from many different fields for periods ranging from 1 day to 3 months, as well as a activities aimed at education and at increasing diversity in mathematics and science. Almost every program combines mathematics and a field of science or engineering; most programs include both pure and applied mathematics; IPAM has focused on important emerging topics, such as proteomics, internet search engines, compressed sensing, nanosystems, virtual surgery, and document space. In programs where there is an emphasis on pure mathematics, IPAM works to create ties between different groups of researchers working on related problems. IPAM's research programs enhance the vitality of mathematics by promoting interactions between different fields of mathematics and between mathematics and science; they promote new research collaborations; they help the career development of graduate students, postdocs and junior faculty; and they launch both junior and senior scientists on new research directions. The net effect is to build new scientific communities that can address the complex scientific challenges of our time. IPAM's education and diversity activities increase the flow of students into the scientific workforce and encourage the full participation of women and underrepresented minorities in mathematics and science. This is of tremendous importance for the vitality of mathematics and science in the broader community.