Operator Algebras in the Twenty-First Century

该奖项用于资助参加于2019年3月30-31日在宾夕法尼亚大学数学系举行的“21世纪的算符代数”会议。会议的重点是分析的最新发展，特别是在算子代数及其在物理学中的应用领域。这次会议的目的是促进算子代数领域本身的发展，并让非专业人士了解这些方法在解决该领域以外的问题方面的力量。几位杰出的数学家已同意出席这次会议并在会上发言。这一奖项为早期职业研究人员、代表性不足群体的成员以及没有其他资金来源的研究人员提供了参加这次会议的机会。算符代数为贯穿整个数学的问题提供了一个强大的视角。这次会议将回顾这一领域的许多成就中的一些，特别是与理查德·V·卡迪森的工作有关的成就，以及它们与当前数学和数学物理中感兴趣的问题的关系。主题包括：与拓扑量子场论的关系，凝聚态物理学的进展，Kadison-Singer猜想，以及非对易几何范例的阐述，该范例将算子代数置于从几何到数学物理，到解析数论和其他领域的问题的中心。更多信息可在会议网站上获得，sitehttps://www.math.upenn.edu/~deturck/kadison-conference/index.htmlThis奖反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides funding for participation in the conference "Operator Algebras in the Twenty-first Century" held March 30-31, 2019 at the Department of Mathematics, University of Pennsylvania. The conference focuses on recent developments in analysis, especially in the field of operator algebras and its applications in physics. The conference aims to facilitate both the growth of the operator algebras field per se, as well as to inform non-specialists of the power of these methods for addressing questions outside of this field. Several distinguished mathematicians have agreed to attend and speak at this conference. This award gives early career researchers, members of underrepresented groups, and researchers without other sources of funding an opportunity to attend and participate in this conference. Operator algebras provide a powerful perspective on problems throughout mathematics. This meeting will review some of the many accomplishments in this field, especially as related to the work of Richard V. Kadison, and their relationships to problems of current interest in mathematics and mathematical physics. Topics include: relations with topological quantum field theory, advances in condensed matter physics, the Kadison-Singer conjecture, and elaboration of the non-commutative geometry paradigm, which places operator algebras at the center of problems in fields from geometry, to mathematical physics, to analytic number theory and beyond. More information is available at the conference web sitehttps://www.math.upenn.edu/~deturck/kadison-conference/index.htmlThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.