Fields Institute Thematic Program: Forcing and its Applications

这笔赠款将为安大略多伦多菲尔兹研究所2012年秋季强迫及其应用专题项目提供补充资金。 50年前，保罗·科恩（Paul Cohen）开发了一种强迫方法来解决希尔伯特的第一个问题：连续统假设的真理性。 今天，这种方法比以往任何时候都更有意义。 虽然它最初是作为元数学工具开发的，但它也被用于解决组合学，泛函分析和拓扑学中出现的问题。 随着该方法的成熟和变得更加强大，其范围和范围已显着扩大。强迫的新方向越来越多地受到越来越广泛的领域中的基本问题的影响。 这些相关领域的惊人突破正受到强迫方法同样令人兴奋的进展的推动。 尽管如此，该方法在很大程度上仍然是集合论内部使用的工具。 该计划旨在进一步发展该方法及其适用性分析，组合学，算子理论，集合论和拓扑学。菲尔兹研究所是世界上首屈一指的数学研究所之一。 每学期它赞助一个主题计划在数学的一个重点子学科，使在该领域的高级领导人与研究生和初级研究人员一起，所有在一个屋檐下。 在2012年秋季，主题计划的重点是科恩的强迫方法。 本学期将有三个重点研讨会和两个学期的研究生课程，都吸引了国际观众。 该计划的主要目标之一是使这一重要技术能够为数学界的更广泛的横截面所用。

This grant will provide supplemental funding to the fall 2012 Thematic Program on Forcing and its Applications at the Fields Institute in Toronto, Ontario. Fifty years ago Paul Cohen developed the method of forcing to solve Hilbert's first problem: the truth of the Continuum Hypothesis. Today this method is more relevant than ever. While it was originally developed as a meta-mathematical tool, it has been also used to solve problems arising in combinatorics, functional analysis, and topology. As the method matured and became even more powerful, its scope and reach has been significantly broadened. New directions in forcing are ever more influenced by fundamental questions in a broadening range of fields. Stunning breakthroughs in these related fields are being propelled by the equally exciting advances in the forcing method. Still, the method has largely remained a tool used internally by set theory. The program aims to further develop the method and its applicability analysis, combinatorics, operator theory, set theory, and topology.The Fields Institute is one of the premier mathematical institutes in the world. Each semester it sponsors a thematic program in a focused sub-discipline of mathematics, bringing senior leaders in the field together with graduate students and junior researchers, all under one roof. In fall 2012, the focus of the thematic program is Cohen's method of forcing. The semester will feature three focused workshops and two semester long graduate courses, all attracting an international audience. One of the primary goals of the program is to make this important technique accessible to a broader cross section of the mathematical community.