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

黎曼曲面族与Weil-Petersson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几何是公认的提供重要信息的几何Teichmuller空间和模空间的黎曼曲面。 在不到十年的时间里，已经有了一系列关于Weil-Petersson几何的突破性工作。 这些作品是基于一系列的方法，因此涉及感兴趣的问题，并为广大观众进一步研究。这次会议将暴露新的学生和开始研究人员在该领域的各种标准化技术。 将介绍一些最近的突破，并讨论开放的研究问题。 这将推动未来十年及以后的进一步研究。 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和硕士水平的学生群体将接触到研究水平的数学，这将鼓励他们继续学习。 我们的许多学生是他们家庭中的第一代，在他们的研究中走到这一步，并且是代表性不足的群体的成员，不幸的是，他们很少接触到这样的机会。

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.