RTG: Geometry, Group Actions, and Dynamics at Wisconsin

威斯康星大学几何、群体行动和动力学研究培训小组（RTG）将以一种专门为各级之间的相互作用和支持而设计的方式，培训本科、研究生、博士后和教师级别的数学早期职业研究人员。该培训将为参与者进一步学习、独立研究、专业发展以及在工业界和学术界的职业生涯做好准备。RTG将支持与威斯康星麦迪逊实验数学实验室合作进行的本科生研究，并作为该实验室的延伸，包括学期项目和夏季研究经验。它将为研究生的研究和专业发展提供支持，并为博士后学者提供支持，以及举办一系列研究研讨会和专业发展研讨会。所有这些支持都将通过RTG提供的强化指导而得到加强，并将在所有级别上建立专业联系和指导关系。附属教师在专业发展，拓展和指导方面拥有丰富的经验，承诺促进和支持传统上得不到支持的人群取得成功。隶属于RTG的教师的学术专长涵盖了分析、几何、群体行为和动力系统等广泛的主题。在RTG下进行的研究将包括诸如平面的统计和动力学性质，双曲群的随机子群的几何，曲面上曲线的组合，随机群，图的分析，低维拓扑和模空间上的动力学等主题。该研究将融入所有参与者的专业发展，在各个层次的研究人员之间建立互动和指导。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The Research Training Group (RTG) in Geometry, Group Actions, and Dynamics at Wisconsin will train early career researchers in mathematics at the undergraduate, graduate, postdoctoral, and faculty levels in a manner designed specifically for mutual interaction and support between all levels. The training will prepare participants for further study, independent research, professional development, and careers in industry as well as the academy. The RTG will support undergraduate research conducted in collaboration with, and as an extension of, the Madison Experiment Mathematics Lab at Wisconsin, both in semester long programs as well as Summer Research Experiences. It will provide support for graduate student research and professional development, and support for postdoctoral scholars, as well as running a series of research workshops and professional development seminars. All of this support will be augmented by the enhanced mentoring afforded by the RTG and will create professional connections and mentorship bonds across all levels. The affiliated faculty have extensive experience in professional development, outreach, and mentorship that promises to foster and support success from traditionally under-supported populations. The academic expertise of the faculty affiliated with the RTG spans a wide array of topics in analysis, geometry, group actions, and dynamical systems. Research conducted under the RTG will include topics such as statistical and dynamical properties of flat surfaces, the geometry of random subgroups of hyperbolic groups, the combinatorics of curves on surfaces, random groups, analysis on graphs, low-dimensional topology, and dynamics on moduli spaces. The research will be integrated into the professional development of all participants, creating interactions and mentorship between researchers at all levels.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.