Combinatorial and Algebraic Aspects of Geometric Structures

该奖项为参加将于2019年7月22日至26日在泰国清迈大学举行的“几何结构的组合和代数方面”会议的美国参与者提供部分支持。本次会议的目的是建立在伊利诺伊大学、清迈大学、新加坡国立大学和卢森堡大学以及更广泛地来自欧洲、亚洲和北美的研究人员之间现有合作的基础上。会议将包括针对研究生和博士后的一般研究讲座和迷你课程讲座，以及由研究生和博士后进行的五分钟闪电演讲，为他们提供分享研究成果并与其他参与者进行对话的机会。该地点将为美国研究人员提供机会，与来自欧洲和亚洲国家的同行建立新的联系，特别是那些来自后者的国家，他们可能无法进行国际旅行。顾名思义，这次会议的主题非常广泛，涉及到流形上的几何结构，包括曲面上的双曲结构和平面结构，由其他李群表示产生的奇异几何结构，以及由几何群论产生的粗糙几何结构。演讲者的选择代表了这个列表中连贯的主题组合，以最大限度地发挥新的合作和领域交叉施肥的潜力。例如，Maloni在双曲和混合特征几何结构方面的研究与Bridgeman和Canary在更高的Teichmueller理论和双曲几何方面的工作非常吻合。PI与来自清迈、泰国、新加坡和卢森堡的研究人员之间的现有合作，以及来自这些地点的研究人员之间的合作，也将为新的合作提供一个起点。关于会议的更多细节可以在会议网站上找到：http://www.math.science.cmu.ac.th/lst/index.phpThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

This award provides partial support to U.S. based participants at a conference titled "Combinatorial and Algebraic Aspects of Geometric Structures" which will be held July 22 through July 26, 2019 at Chiang Mai University, in Chiang Mai, Thailand. This conference aims to build on existing collaborations between researchers at the University of Illinois, Chiang Mai University, National University of Singapore, and the University of Luxembourg, and more broadly from Europe, Asia, and North America. The conference will include general research talks and mini-course lectures aimed at graduate students and postdocs, as well as five-minute lightning talks by graduate students and postdocs, providing them an opportunity to share their research and spark conversations with other participants. The venue will provide the opportunity for US researchers to make new connections with their counterparts from European and Asian countries, in particular those from the latter countries for whom it may not be feasible to travel internationally. The theme of the conference, as the title suggests, is quite broad and involves topics such as geometric structures on manifolds, including hyperbolic and flat structures on surfaces, exotic geometric structures arising from representations into other Lie groups, and coarse geometric structures arising from geometric group theory. The speakers are chosen to represent a coherent mix of topics from this list, to maximize the potential for new collaborations and cross-fertilization of areas. For example, Maloni's research is in both hyperbolic and mixed-signature geometric structures meshes very well with Bridgeman and Canary's work on higher Teichmueller theory as well as hyperbolic geometry. Existing collaborations between the PI and researchers from Chiang Mai, Thailand, Singapore, and Luxembourg, as well as collaborations between researchers from those locations, will also provide a starting point for new collaborations. Additional details about the conference can be found on the conference website: http://www.math.science.cmu.ac.th/lst/index.phpThis 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.