University of Pennsylvania RTG in Mathematical Physics

该项目垂直整合了宾夕法尼亚大学数学系数学物理、几何和弦理论的研究和培训。宾夕法尼亚大学集团将开展一系列培训活动，包括研究生暑期学校、研究和外展研讨会、开发新的研究生和本科课程以及准备课程材料，包括研究生教科书。与此同时，将开发三个垂直研究项目：几何朗兰兹计划与量子场论和弦理论的对偶性之间令人兴奋的新联系；重整化群流对超对称量子场论模量作用的几何和数值研究；以及对特殊完整度量的探索。该小组将创造一个肥沃的教育环境，向不同预备水平的美国学生介绍高能物理数学方面的前沿研究问题。数学物理是当今数学和物理最活跃的分支之一，与数学和科学的其他分支的联系越来越重要。该项目活动旨在增加积极探索数学物理、几何和弦理论的美国人的数量和多样性，并提高他们的体验质量。预计各个层面都会有很大的进步，研究生和博士后研究的进步非常显着。人们对宇宙理论的兴趣爆炸式增长，使得现在成为开始该领域研究的一个非常令人兴奋的时刻，但这也让年轻的研究人员入门变得困难。该项目将增加数学物理、几何和弦理论方面受过广泛训练的研究人员的流动，从而增强二十一世纪数学这些重要领域的培训基础设施和研究人员队伍。

This project vertically integrates research and training in Mathematical Physics, Geometry, and String Theory at the Mathematics Department of the University of Pennsylvania. The Penn group will undertake a series of training activities including graduate summer schools, research and outreach workshops, the development of new graduate and undergraduate courses, and preparation of course materials, including a graduate textbook. In parallel, three vertical research projects will be developed: the exciting new connections between the Geometric Langlands Program and dualities in quantum field theory and string theory; a geometric and numerical investigation of the action of the renormalization group flow on the moduli of supersymmetric quantum field theories; and an exploration of special holonomy metrics. The group will create a fertile educational environment that will introduce US students of various preparation levels to cutting edge research questions in the mathematical aspects of high energy physics.Mathematical Physics is one of the most active branches of mathematics and physics today, with increasingly important connections to other branches of mathematics and science. The project activities are designed to increase the number and the diversity of Americans who are actively exploring Mathematical Physics, Geometry, and String Theory, and to improve the quality of their experience. Strong improvements are anticipated at all levels, with very significant improvements in graduate and postdoctoral research.. The explosive growth of interest in the theory of universe has made this a very exciting time to begin research in the field, but it has also made it difficult for young researchers to get started. This project will increase the flow of broadly trained researchers in Mathematical Physics, Geometry, and String Theory, therefore enhancing the training infrastructure and the research workforce in these vital areas of mathematics in the twenty-first century.