CBMS Regional Conference in the Mathematical Sciences - "Families of Riemann surfaces and Weil-Petersson Geometry'' - Summer 2009; New Britain, CT

项目摘要黎曼曲面族和魏尔-彼得森几何黎曼曲面的几何和变形理论的研究长期以来被认为涉及广泛的概念和广泛的技术。Weil-Petersson几何被认为提供了关于Teichmuller空间和Riemann曲面的模空间的几何的重要信息。在不到十年的时间里，出现了一系列关于韦尔-彼得森几何的突破性成果。这些作品基于一系列的方法，因此涉及广泛的受众感兴趣和进一步研究的问题。这次会议将使新的学生和刚开始的研究人员接触到该领域的各种标准化技术。一些最近的突破将被介绍，开放的研究问题将被讨论。这将推动未来十年乃至更长时间的进一步研究。此外，通过在中央康涅狄格州立大学举行这次会议，一个非常多样化的本科生和MasterÕs水平的学生群体将接触到研究水平的数学，这将鼓励他们继续他们的学习。我们的许多学生是他们家族中第一代在学业上走到这一步的人，他们是代表性不足的群体的成员，不幸的是，他们很少有机会接触到这样的机会。

Project AbstractFamilies of Riemann surfaces and Weil-Petersson GeometryThe investigation of the geometry and deformation theory of Riemann surfaces is long recognized for involving a wide range of concepts and a wide range of techniques. The Weil-Petersson geometry is recognized for providing important information on the geometry of both the Teichmuller space and the moduli space of Riemann surfaces. In less than a decade there have been a collection of breakthrough works on Weil-Petersson geometry. The works are based on a range of approaches and so involve matters of interest and further study for a broad audience.This conference will expose new students and beginning researchers to a variety of standardized techniques in the field. A number of very recent breakthroughs will be introduced, and open research questions will be discussed. This will drive further research over the next decade and beyond. In addition, by having this conference at Central Connecticut State University, a very diverse group of undergraduate and MasterÕs level students will be exposed to research level mathematics, which will encourage them to continue their studies. Many of our students are the first generation in their families to get this far in their studies, and are members of underrepresented groups, who are unfortunately rarely exposed to opportunities such as this.