Geometry and Physics EMSW21-RTG

AbstractAward：DMS-0636646首席研究员：Ezra Getzler，Boris Tsygan，Eric Zaslow现代数学物理学越来越多地从广泛的数学学科中汲取技术。 微分几何通过指数理论、微局域分析和镜像对称在量子场论的研究中起着至关重要的作用。同伦理论通过A-无穷范畴和导出范畴的工具，已经成为几何和物理研究中的一个重要工具。 通过朗兰兹纲领和几何朗兰兹纲领之间的类比，表示论和数论一直在发展与共形场论的联系。西北大学很幸运地拥有这些研究方向的世界领导者。这个小组的目标是在培养这些领域的学生和博士后研究人员方面取得国家领导地位。物理世界用数学语言书写其定律，物理学的进步与数学方法和理论的发展密切相关。在当代数学物理学中，几何学以许多不同的形式和表示论（对称性的研究）起着中心作用。西北大学的数学物理学研究组在实现增加从事数学物理学职业的美国公民数量的目标方面处于特别有利的地位：该大学吸引了一批特别强大的本科生（通过其著名的综合科学计划，例如）;研究生课程有更多的选择性;数学系还开发了博士后项目，该项目一直成功地吸引了女性，并一直将博士后置于不成功的学术职位。

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.