3-Manifolds, Artin Groups, and Cubical Geometry

3-流形、Artin群和立方几何

• 批准号: 1040900
• 负责人: Jason Behrstock
• 金额: $ 4.12万
• 依托单位: Research Foundation Of The City University Of New York (Lehman)
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1040900&HistoricalAwards=false
• 关键词: Manifolds; Artin; Groups; Cubical; Geometry

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.

NSF/CBMS区域数学科学会议3-流形、阿丁群和三次几何2011年6月13-17日纽约市立大学研究生中心首席讲师：丹尼尔T。怀斯全职教授麦吉尔大学数学与统计系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3-流形拓扑中出现的某些长期悬而未决的问题。这项工作已经成熟，在过去的几年中，一个强大的和连贯的理论，将重新定位在这一领域的研究。最近的成就包括证明Baumslag的1967年猜想，一个关系群的挠是剩余有限的，证明哈肯双曲3-流形实际上是纤维（出乎意料地证实了一个猜想瑟斯顿的从20世纪80年代），和惊人的认识，即一个大的swath提出的团体所产生的几何群论实际上是几乎子群的直角阿廷集团。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，这个主题已经被证明是非常肥沃的地形和新的研究人员肯定会把事情带到一个新的水平，无论是在简化和扩展的范围内的一些证明，并在争取新的应用在邻近领域。本次会议将解决广泛的学生和年轻的研究人员，包括那些有兴趣在3-流形拓扑和几何群论。在纽约城市大学研究生中心举行会议也将有助于与会者的多样性。纽约市立大学是美国最大的城市大学，研究生中心是其博士中心。授予机构。大多数纽约市立大学的学生自我认同为非洲裔美国人或西班牙裔，大约60%是女性。