CBMS Conference: Topological and Geometric Methods in Quantum Field Theory NSF-CBMS Regional Conference in the Mathematical Sciences

CBMS 会议：量子场论中的拓扑和几何方法 NSF-CBMS 数学科学区域会议

• 批准号: 1642636
• 负责人: David Ayala
• 金额: $ 3.5万
• 依托单位: Montana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-12-15 至 2017-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1642636&HistoricalAwards=false
• 关键词: CBMS; Conference; Topological; Geometric; Methods

A NSF-CBMS regional conference on "Topological and geometric methods in quantum field theory" will be held July 31- August 4, 2017 at Montana State University (Bozeman). Topological phases of matter are at the frontline of research in condensed matter physics and offer new possibilities in electronics and superconductors. Topological phases of matter - and more generally, quantum field theory - have elegant formulations in terms of pure mathematics, specifically from the fields of geometry (the study of objects via measuring lengths, areas, etc.) and topology (the study of more global quantity of objects which are intrinsic to the space and not dependent on lengths, etc.). Moreover, insight and imagination in physics has led to many mathematical advances in geometry and topology. Recently, mathematicians have undertaken a program to classify and exemplify all possible topological phases of matter. The main goal of the conference is to explain the interplay between physics and mathematics described above and to encourage further interaction and dialogue between condensed matter physicists, and geometers and topologists. In particular, the conference is aimed at young researchers (graduate students and postdoctoral fellows) in order to energize and educate a future generation. Further, it is an explicit goal of the conference to engage women and underrepresented mathematicians and physicists, as well as the research communities of the Northern Rocky Mountains, in these exciting developments. The conference will result in a monograph which will fill a gap in the academic literature concerning the interface of geometry and topology with physics.The classification of topological phases has been a hot topic in the last five years, and it's relationship to stable homotopy theory and bordism groups was realized early on. The recent work of Freed and others recognizes certain topological phases as invertible representations of bordism categories. Recent work of Galatius, Lurie, and others realizes the classification of such representations as an accessible computation in stable homotopy theory. Specifically, for instance, the groupoid completion of the bordism n-category is the (-n)-space of the Thom spectrum of the virtual negative of the universal rank n bundle. Understanding topological quantum field theory in terms of bordism categories has come a long way since its introduction by Atiyah in the 1980's. The consideration of 3d Chern-Simons theory in the 1990's made it clear that an extension to higher category theory was necessary. The subsequent development of higher category theory and derived geometry has ushered in a flourish of activity in topological quantum field theory, particularly since Lurie's inspired outline of the cobordism hypothesis in 2010. These developments are still underway and being consolidated by the mathematics community; this conference will go a long way in demonstrating their power and breadth.Further information can be found at the conference website: http://www.math.montana.edu/cbms/

关于“量子场论中的拓扑和几何方法”的NSF CBMS区域会议将于2017年7月31日至8月4日在蒙大拿州立大学（波兹曼）举行。物质的拓扑相是凝聚态物理学研究的前沿，为电子学和超导体提供了新的可能性。物质的拓扑相--更一般地说，量子场论--在纯数学方面有着优雅的公式，特别是在几何学领域（通过测量长度、面积等来研究物体）。和拓扑学（研究更多的全球数量的对象是内在的空间和不依赖于长度等）。 此外，物理学中的洞察力和想象力导致了几何和拓扑学中的许多数学进步。 最近，数学家们开始了一项计划，对物质的所有可能的拓扑相进行分类和计算。会议的主要目标是解释上述物理学和数学之间的相互作用，并鼓励凝聚态物理学家，几何学家和拓扑学家之间的进一步互动和对话。 特别是，会议的目标是年轻的研究人员（研究生和博士后研究员），以激励和教育下一代。此外，会议的一个明确目标是让妇女和代表性不足的数学家和物理学家以及北方落基山脉的研究社区参与这些令人兴奋的发展。这次会议将产生一本专著，填补有关几何和拓扑学与物理学接口的学术文献的空白。拓扑相的分类在过去五年中一直是一个热门话题，它与稳定同伦理论和边群的关系很早就被认识到，Freed等人最近的工作承认某些拓扑相是边群的可逆表示，类别 最近的工作加拉休斯，卢里，和其他人实现了分类，这种表示作为一个可访问的计算在稳定同伦理论。 具体地说，例如，边数n-范畴的广群完备化是泛秩n丛的虚负数的Thom谱的（-n）-空间。理解拓扑量子场论的边界范畴已经走了很长的路，因为它介绍了阿蒂亚在20世纪80年代。 20世纪90年代对3d Chern-Simons理论的考虑清楚地表明，扩展到更高的范畴理论是必要的。 随后的发展更高的范畴理论和衍生几何迎来了蓬勃发展的活动在拓扑量子场论，特别是因为卢里的灵感大纲的协边假说在2010年。 这些发展仍在进行中，并正在由数学界巩固;这次会议将在很大程度上展示他们的力量和广度。更多信息可以在会议网站上找到：http://www.math.montana.edu/cbms/