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

《量子场论中的拓扑和几何方法》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NSF-CBMS地区会议。物质的拓扑相是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--更广泛地说，量子场论--在纯数学方面有着优雅的表述，特别是在几何领域(通过测量长度、面积等来研究物体)。和拓扑学(对空间固有的、不依赖于长度等的更多全局数量的对象的研究)。此外，物理学中的洞察力和想象力导致了几何学和拓扑学的许多数学进步。最近，数学家们开展了一项计划，对物质所有可能的拓扑相进行分类和举例说明。这次会议的主要目的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、地质学家和拓扑学家之间的进一步互动和对话。该会议特别针对年轻的研究人员(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落基山脉的研究界参与这些令人兴奋的发展。这次会议将产生一部专著，填补关于几何和拓扑与物理界面的学术文献的空白。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界群的关系很早就认识到了。Freed等人最近的工作承认，某些拓扑学阶段是边界主义范畴的可逆表示。Galatius，Lurie等人最近的工作实现了将这类表示归类为稳定同伦理论中的可达计算。具体地说，例如，边界n-范畴的群仿完备化是泛秩n-丛的虚负的Thom谱的(-n)-空间。从20世纪80年代阿提亚提出的拓扑型量子场论到20世纪80年代的S，从边界范畴的角度来理解拓扑型量子场论已经取得了长足的进步，而90年代S对3DChern-Simons理论的研究表明，扩展到更高的范畴理论是必要的。高级范畴理论和衍生几何的发展带来了拓扑量子场论的蓬勃发展，特别是自2010年Lurie提出协边假说的启发大纲以来。这些发展仍在进行中，并得到数学界的巩固；这次会议将大大有助于展示它们的力量和广度。欲了解更多信息，请访问会议网站：http://www.math.montana.edu/cbms/

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/