Workshop on Geometric Group Theory

该奖项支持参加2010年8月9日至14日在印度果阿大学举行的“几何群论研讨会”的美国特邀演讲者和美国初级研究人员。这将是国际数学家大会(ICM)的一个卫星会议。研讨会将以各种主题为特色，这些主题体现了该领域的中心主题，即通过将群体视为几何对象来处理群体理论问题。将有关于李群、CAT(0)群和OUT(FN)中晶格的迷你课程，这些课程将针对研究生和该领域的新手研究人员。此外，还将有约17个应邀研究讲座，涉及这些领域以及与之密切相关的领域，如映射类群、极限群、相对双曲群和准等距刚性。几何群论是近年来蓬勃发展的一个相对较新的领域。几何群论中的问题和技巧来自令人震惊的范围：组合群论、三流形、黎曼几何、逻辑和代数几何只是其中的几个例子。该领域的跨学科方面已经产生了丰富的理论。这个研讨会将创建一个激发新想法的论坛，通过聚集各种参与者：领先的专家，初级研究人员，以及来自相关领域的研究人员，但传统上不是几何群论的一部分。预计这将是互惠互利的：来自不同背景的技术、工具和想法的共享可能会带来有趣的新研究途径。此外，它将对国际合作产生积极影响。研讨会还将寻求通过提供该领域研究现状的全面图景来吸引优秀的数学家对几何群论感兴趣。这将通过侧重于关键范例和鼓舞人心的想法的小型课程和应邀的研究讲座来完成。还将有简短的演讲，这将为年轻数学家提供一个展示他们研究成果的平台。

This award supports US invited speakers and US junior researchers attending the "Workshop on Geometric Group Theory", to be held August 9-14, 2010 at Goa University in India. This will be a satellite conference of the International Congress of Mathematicians (ICM). The workshop will feature a variety of topics which exemplify the central theme of the field, that of approaching group theoretic questions by treating groups as geometric objects. There will be mini-courses on lattices in Lie groups, CAT(0) groups and Out(Fn), which will be aimed at graduate students and researchers new to the field. In addition, there will be about 17 invited research talks in these as well as closely related areas, such as mapping class groups, limit groups, relatively hyperbolic groups and quasi-isometric rigidity.Geometric group theory is a relatively new field which has been flourishing in recent years. Questions and techniques in geometric group theory come from a startling range of sources: combinatorial group theory, three-manifolds, Riemannian geometry, logic, and algebraic geometry are just a few examples. The interdisciplinary aspect of the field has given rise to a rich theory. This workshop will create a stimulating forum for generating new ideas, by bringing together a variety of participants: leading specialists, junior researchers, and researchers from fields that are related, but not traditionally a part of geometric group theory. This is expected to be mutually beneficial: the sharing of techniques, tools and ideas from different backgrounds is likely to lead to interesting new avenues of research. Further, it will have a positive impact on international collaborations. The workshop will also seek to attract good mathematicians to geometric group theory by providing a well-rounded picture of the current state of research in the field. This will be done through mini-courses which focus on key examples and motivating ideas, and through invited research talks. There will also be short contributed talks, which will provide a platform for young mathematicians to present their research.