3-Manifolds, Artin Groups, and Cubical Geometry

NSF/CBMS数学科学区域会议-流形、Artin群和三次几何JUNE 13-17,2011年纽约城市大学研究生中心首席讲师：Daniel T.Wise麦吉尔大学数学和统计系全职教授怀斯教授的讲座将讨论几何群论中一系列相互关联的技术和定理，旨在解决组合群论和三维流形拓扑中出现的某些长期悬而未决的群问题。在过去的几年里，这项工作已经成熟，形成了一个强大而连贯的理论，将重新定位这一领域的许多研究。最近的成果包括证明了Baumslag1967年的猜想，即有挠的一相关子群是剩余有限的，证明了Haken双曲3-流形是虚拟纤维的(出人意料地证实了瑟斯顿从1980年的S提出的一个猜想)，以及令人震惊的认识：几何群论中出现的大量有限表示群实际上是直角Artin群的虚拟子群。现在是时候评估这里的发展，并教育进入这一领域的下一代研究人员。事实上，这一学科已经被证明是非常肥沃的领域，新的研究人员肯定会把事情带到一个新的水平，无论是在简化和扩大一些证明的范围方面，还是在努力在邻近领域寻求新的应用方面。这次会议将介绍广泛的学生和年轻的研究人员，包括那些对3-流形拓扑学和几何群论感兴趣的人。在纽约市立大学研究生中心举行会议也将有助于增加与会者的多样性。CUNY是美国最大的城市大学，研究生中心是它的中心博士授予机构。纽约州立大学的大多数学生都认为自己是非裔美国人或西班牙裔，大约60%是女性。

NSF/CBMS REGIONAL CONFERENCE IN THE MATHEMATICAL SCIENCES3-MANIFOLDS, ARTIN GROUPS, AND CUBICAL GEOMETRYJUNE 13-17, 2011CITY UNIVERSITY of NEW YORK GRADUATE CENTERPrincipal Lecturer:Daniel T. WiseFull ProfessorDepartment of Mathematics and StatisticsMcGill UniversityThe lectures of Professor Wise will treat a body of interrelated techniques and theorems in geometric group theory that are aimed at resolving certain long-standing open problems on groups arising in combinatorial group theory and 3-manifold topology. This work has matured during the past few years to apowerful and coherent theory that will reorient much of the research in this area. Recent achievements include a proof of Baumslag's 1967 conjecture that one-relator group with torsion are residually finite, a proof that Haken hyperbolic 3-manifolds are virtually fibered (unexpectedly confirming a conjecture of Thurston's from the 1980's), and the stunning realization that a large swath of the finitely presented groups arising in geometric group theory are actually virtually subgroups of right-angled Artin groups. It is now time to take stock of the developments here, and educate the next generation of researchers entering this area. Indeed, this subject has proven to be extremely fertile terrain and new researchers are certain to take things to the next level, both in simplifying and extending the reach of some of the proofs, and in striving for novel applications in neighboring fields. This conference will address a broad collection of students and young researchers, including both those with interest in 3-manifold topology and geometric group theory. Having the conference at the City University of New York Graduate Center will also contribute to the diversity of the participants. CUNY is the largest urban university in the United States and the Graduate Center is its central Ph.D. granting institution. A majority of CUNY students are self-identified as African-American or Hispanic and approximately 60% are female.