Special Meeting: Foundations of Computational Mathematics

这个主题计划将探索数学和计算之间不断发展的接口。 涉及到各种各样的数学学科，包括计算代数几何和符号计算，计算数论，计算几何，拓扑学和动力学，复杂性和可计算性在真实的计算，计算机科学和优化理论。 算法将是中心，不仅在其传统的作用，在发明和分析的数值方法，但也作为基本的理论工具，数学实验和发现，作为证明技术，并作为模型的可计算性和易处理性。 通过聚集一个大的，广泛的参与者群体，从建立数学家和计算机科学家到研究生，该计划将改变我们的计算数学知识很好地走向未来。在多伦多的菲尔兹研究所将主办这个及时的六个月的计划，利用快速发展的网络连接数学和计算的国际专业知识; NSF的资金将支持美国初级研究人员和研究生的参与。 不断增加的计算能力对应用数学，科学和工程的影响，受到加密，数据挖掘和网络搜索等新应用的推动，不可避免地导致了对计算工具本身的研究，创造和振兴了丰富的数学学科，广泛代表了这个特殊的学期。 该计划包括三个为期一周的重点研讨会，特别讲座系列和研究生课程（特别是由两位杰出的美国女性计算机科学家伊娃塔尔多斯和勒诺布鲁姆提供），不同的高级和初级研究人员和博士后研究员进行长期和短期访问，并从事日常互动，并广泛努力传播新兴的新科学。 这些多样化的活动将整合尖端研究，跨学科协同作用，以及尽可能广泛和包容的参与者的学习和培训机会。

This thematic program will explore the evolving interface between mathematics and computation. A wide variety of mathematical disciplines are involved, including computational algebraic geometry and symbolic computation, computational number theory, computational geometry, topology and dynamics, complexity and computability in real computation, computer science and optimization theory. Algorithms will be central, not only in their traditional role in the invention and analysis of numerical methods, but also as fundamental theoretical tools for mathematical experimentation and discovery, as proof techniques, and as models of computability and tractability. By assembling a large, broad group of participants, ranging from established mathematicians and computer scientists to graduate students, the program will transform our knowledge of computational mathematics well into the future.The Fields Institute in Toronto will host this timely six-month program, capitalizing on rapidly evolving networks of international expertise linking mathematics and computation; NSF funding will support participation of junior U.S. researchers and graduate students. The impact of constantly increasing computational power on applied mathematics, science and engineering, motivated by new applications such as encryption, data mining, and web search, has inevitably led to the study of the computational tools themselves, creating and reinvigorating a rich spectrum of mathematical disciplines broadly represented at this special semester. The program involves three one-week focus workshops, special lecture series and graduate courses (delivered in particular by two distinguished U.S. female computer scientists, Eva Tardos and Lenore Blum), diverse senior and junior researchers and postdoctoral fellows making long- and short-term visits and engaging in day-to-day interaction, and extensive efforts to disseminate the emerging new science. These diverse activities will integrate cutting-edge research, interdisciplinary synergy, and learning and training opportunities for an array of participants as broad and inclusive as possible.