Geometry and Physics EMSW21-RTG

摘要奖：DMS-0636646主要研究员：Ezra Getzler，Boris Tsygan，Eric Zas low现代数学物理越来越多地从广泛的数学学科中汲取技术。通过指数理论、微域分析和镜像对称性，微分几何在量子场论的研究中起着至关重要的作用。通过A-无穷范畴和派生范畴的工具，同伦理论已经成为几何和物理研究中的重要工具。通过类比朗兰兹程序和几何朗兰兹程序，表象理论和数论一直在发展与保形场理论的联系。西北大学很幸运，它的教职员工在这些研究方向上都有世界领先者。这个团体的雄心是在培养这些领域的学生和博士后研究人员方面取得全国领先地位。物理世界用数学语言写下了它的规律，物理学的进步与数学方法和理论的发展密切相关。在当代数学物理中，许多不同形式的几何和表象理论(对称性研究)扮演着中心角色。西北大学的数学物理小组在实现增加从事数学物理职业的美国公民数量这一目标方面处于有利地位：该大学吸引了特别强大的本科生群体(例如，通过其著名的综合科学项目)；研究生项目变得更加挑剔；数学系开发了博士后项目，该项目一直成功地吸引女性，并一直将博士后安置在不成功的学术职位上。

AbstractAward: DMS-0636646Principal Investigator: Ezra Getzler, Boris Tsygan, Eric ZaslowModern mathematical physics increasingly draws its techniquesfrom a broad array of mathematical disciplines. Differentialgeometry plays a vital role in the study of quantum field theorythrough index theory, microlocal analysis, and mirrorsymmetry. Homotopy theory has become an essential tool in thestudy of geometry and physics, through the tools of A-infinitycategories and derived categories. Representation theory andnumber theory have been developing links with conformal fieldtheory through analogies between the Langlands program and thegeometric Langlands program. Northwestern University is fortunateto have on its faculty world leaders in each of these directionsof research. It is the ambition of this group to attain nationalleadership in training students and postdoctoral researchers inthese fields.The physical world writes its laws in the language ofmathematics, and progress in physics is intimately connected toprogress in the development of mathematical methods andtheories. In contemporary mathematical physics, geometry, in manydifferent forms, and representation theory (the study ofsymmetry) play a central role. The mathematical physics group atNorthwestern is particularly well-placed to attain its goal ofincreasing the number of US citizens who pursue careers inmathematical physics: the university attracts a particularlystrong group of undergraduates (through its renowned IntegratedScience Program, for example); the graduate program has becomemore selective; and the mathematics department has developed apostdoctoral program, which has been consistently successful atattracting women and has consistently placed postdocs insuccessful academic positions.