IV Latin-American Congress on Lie Groups and Geometry

该奖项旨在支持参加2012年8月27日至31日在墨西哥瓜纳华托举行的第四届拉丁美洲李群和几何大会的美国参与者。几何中李群的研究历史悠久，由Sophus Lie、Felix Klein、Wilhelm Killing、Elie Cartan、Hermann Weyl等人发展而来。Klein特别提出，指定一个适当的变换群，使某些几何对象保持不变，人们就会观察到各种几何。在全局水平上，每当李群作用于几何对象，如黎曼流形时，这种作用提供了一种刚度度量，并根据其在张量、上同调群等上的表示理论产生了丰富的代数结构。会议的科学焦点是李群论、几何和拓扑学在最广泛意义上的相互作用。会议将讨论以下议题：无穷维李代数及其在几何和拓扑上的应用，流形上作为函数空间的无穷维表示，实半单李群和可积系统的表示理论，映射类群在表面群的表示变体上的作用，特殊完整，Minkowski空间上的适当仿射作用，李群及其算术子群，齐次空间的镶嵌，单幂动力学，第四届拉丁美洲李群与几何大会的目的是向高级和初级数学家传播该领域的最新发展。这次会议将汇集来自拉丁美洲，美国和欧洲的研究人员，他们在不同的方面使用李群相关的不同领域工作，即几何，拓扑，代数等。它还将提高人们对拉丁美洲优秀学术工作的认识，并为研究人员和学生提供交流机会。研究生和博士后将特别受益于与资深数学家的互动。在发展中国家工作的科学家将有机会与来自美国和欧洲的同行进行互动。https://sites.google.com/site/4liegroupsandgeometry/home

This award is to support participants from the US attending the IV Latin-American Congress on Lie Groups and Geometry in CIMAT, Guanajuato, Mexico, August 27-31, 2012. The study of Lie groups in Geometry has a long history, developed by figures such as Sophus Lie, Felix Klein, Wilhelm Killing, Elie Cartan, Hermann Weyl, etc. In particular, Klein proposed that specifying an appropriate transformation group leaving certain geometric objects invariant, one would then observe various geometries. At the global level, whenever a Lie group acts on a geometric object, such as a Riemannian manifold, this action provides a measure of rigidity and yields a rich algebraic structure in terms of its Representation Theory on tensors, cohomology groups, etc. The scientific focus of the conference is the interaction between Lie Group Theory, Geometry and Topology in the broadest possible sense. Topics to be touched upon in the conference will be: infinite-dimensional Lie algebras and their applications to geometry and topology, infinite dimensional representations as spaces of functions on a manifold, representation theory of Real Semisimple Lie Groups and Integrable Systems, actions of the mapping class group on the representation varieties of surface groups, special holonomy, proper affine actions on Minkowski space, Lie groups and their arithmetic subgroups, tessellations of homogeneous spaces, unipotent dynamics, etc.The aim of the fourth Latin-American Congress on Lie Groups and Geometry is to disseminate the latest developments in the area to both senior and junior mathematicians. This meeting will bring together researchers from all over Latin-America, USA and Europe, working in diverse areas related by their use of Lie groups in their different facets, namely geometrical, topological, algebraic, etc. It will also raise awareness of the excellent academic work taking place in Latin America and provide a networking opportunity for researchers and students. Graduate students and postdocs will especially benefit from the interaction with the senior mathematicians. Researchers working in developing countries will have the chance to interact with their counterparts from the USA and Europe. https://sites.google.com/site/4liegroupsandgeometry/home