Quiver Gauge Theory, String Theory and Quantum Field Theory.

学生将学习箭图规范理论的主题，并试图扩展关于这类具有8个超电荷的超对称规范理论的知识。箭图规范理论的技术近年来被用于更好地理解各种量子规范理论的模空间的几何；Hasse图、单极子公式、箭图减法和加法、离散规范和超Kähler商以及3D镜像对称性都是这样的例子。箭图规范理论还具有重要的数学意义-箭图语言为探索几何空间提供了不同的渠道，并经常为数学家的形式方法提供不同的视角。在过去的几年里，箭图被用于研究三维、五维和六维的规范理论。在相关的膜装置中，Hanany-Witten转变被用来理解不同的相及其相关的物理。目前的工作包括在六维空间中扩展“负膜”设置、超Kähler商和离散测量，从而扩展了对不同理论的模空间如何相互关联的理解。

The student will study topics in quiver gauge theory and will attempt to expand the knowledge on this class of supersymmetric gauge theories with 8 supercharges.The techniques of quiver gauge theory have been used in recent years to better understand the geometry of the moduli space of various quantum gauge theories; Hasse diagrams, the monopole formula, quiver subtraction and addition, discrete gauging and hyper-Kähler quotients, and 3d mirror symmetry are some such examples.Quiver gauge theory also has important implications for mathematics - the language of quivers provides a different channel to probe geometric spaces and often offers a different perspective to the formal approach of the mathematician.In the past few years, quivers have been used to study gauge theories in, for example, three, five and six dimensions. In the associated brane setups, the Hanany-Witten transition is used to understand different phases and their associated physics. Current work includes extensions to the 'negative brane' setup in six dimensions, hyper-Kähler quotients and discrete gauging, expanding understanding of how the moduli spaces of different theories relate to each other.