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/

NSF-CBMS 关于“量子场论中的拓扑和几何方法”的区域会议将于 2017 年 7 月 31 日至 8 月 4 日在蒙大拿州立大学（博兹曼）举行。物质的拓扑相处于凝聚态物理研究的前沿，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——在纯数学方面有优雅的表述，特别是来自几何学领域（通过测量长度、面积等来研究物体）和拓扑学领域（研究更全局的物体）空间固有的物体数量，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学和拓扑学方面的许多数学进步。 最近，数学家开展了一项计划，对物质所有可能的拓扑相进行分类和举例说明。会议的主要目标是解释上述物理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进一步的互动和对话。 该会议特别针对年轻研究人员（研究生和博士后），以激励和教育下一代。此外，会议的一个明确目标是让女性和代表性不足的数学家和物理学家以及北落基山脉的研究界参与这些令人兴奋的发展。会议将出版一本专着，该专着将填补几何和拓扑与物理学接口方面的学术文献空白。拓扑相的分类是近五年来的热门话题，它与稳定同伦理论和拓扑相的分类是近五年来的热门话题。边界群很早就被实现了。弗里德和其他人最近的工作将某些拓扑相视为边界范畴的可逆表示。 Galatius、Lurie 和其他人最近的工作将此类表示的分类实现为稳定同伦理论中的可访问计算。 具体来说，例如，Bordism n 范畴的群形完备性是全称秩 n 丛的虚负的 Thom 谱的 (-n)-空间。自从 Atiyah 在 1980 年代提出拓扑量子场论以来，从边界范畴的角度理解拓扑量子场论已经取得了长足的进步。 1990 年代对 3d Chern-Simons 理论的考虑清楚地表明，扩展到更高范畴理论是必要的。 随后高范畴论和派生几何的发展迎来了拓扑量子场论活动的繁荣，特别是自从 Lurie 在 2010 年提出共边假说的启发性概述以来。这些发展仍在进行中，并被数学界巩固；这次会议将在展示其力量和广度方面大有帮助。更多信息可以在会议网站上找到：http://www.math.montana.edu/cbms/