Fields Institute Thematic Program: Forcing and its Applications

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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.