Conference on Representations of Algebras and Related Topics, July 15 - August 10, 2002, Toronto, Canada

2002年7月15日至8月10日，加拿大多伦多举行的关于代数和相关话题的国际会议国际联合会和组委会计划为尽可能多的美国年轻数学家参加今年夏天在多伦多举行的两年一度的国际会议提供支持。除了前沿研究的介绍外，还有几个由顶尖专家进行的系列综述讲座和一个广泛的研讨会计划，旨在向该领域的初创企业研究人员介绍。中心主题是模簇的几何、不变量和变形、同调发展--具体地说，派生范畴、表示类型，包括对驯服或野生代数的枢轴类的深入探索。在这些应用中--他们详尽的文档是最优先的--是复半单李代数和代数群的理论，倒叶的奇点和范畴，对Bernstein-Gelfand-Gelfand范畴结构的新见解，以及有限群模式的同调处理。代数的表示理论起源于对‘群’的研究，最初是允许连接和求逆的某些空间运动的集合。下一个想法是表示更抽象的代数对象，例如，在理论物理和化学中，用合适空间的线性运动来表示，使它们的结构更加透明。与此同时，沿着这条线研究的对象的范围已经大大扩大，并汇集了大量分析这种表征的方法。已证明特别有效的工具包括几何和组合设置，以及可概括如下的一般主题的变化：一是从建立可以完全分析的最优情况开始，然后测量更具挑战性的情况与最优情况的偏差，以取得进展，以应对复杂性的逐步增加。应用几乎扩展到数学的所有部分，并为理论物理中的模型提供理论框架。事实上，最近的一些倡议是由物理学家推动的，并反馈到量子物理学。

International Conference on Representations of Algebras and RelatedTopics, July 15 -- August 10, 2002, Toronto, CanadaThe PI and the organizing committee plan to provide support for theparticipation of as many junior US mathematicians as possible in thebiennial international meeting in Toronto this summer. Next to thepresentation of cutting-edge research, several series of overviewlectures by leading experts and an extensive workshop program aimat introducing start-up researchers to the field. Central subjectsare the geometry of module varieties, invariants and deformations,homological developments -- specifically, derived categories,representation type, including the in-depth exploration of pivotalclasses of tame or wild algebras. Among the applications -- theirthorough documentation is one of the highest priorities -- are thetheories of complex semisimple Lie algebras and algebraic groups,singularities and categories of perverse sheaves, new insights intothe structure of the Bernstein-Gelfand-Gelfand category, as wellas the homological treatment of finite group schemes.The representation theory of algebras has its origin in the studyof 'groups', originally certain collections of motions of spacewhich allow for concatenation and inversion. The next idea was torepresent more abstract algebraic objects, arising in theoreticalphysics and chemistry for instance, in terms of linear motions ofsuitable spaces, to render their structure more transparent. In themeantime, the scope of objects studied along this line has beendramatically enlarged, and a big arsenal of methods to analyze suchrepresentations has been assembled. Tools which have provedparticularly effective include geometrical and combinatorialsetups, and variations of a general theme which can be outlined asfollows: One starts by establishing optimal situations, which canbe completely analyzed, and then measures the deviation of a morechallenging situation from the optimal ones to make headway insteps dealing with progressive increases in complexity.Applications extend to almost all parts of mathematics and providethe theoretical frames for models in theoretical physics.In fact, some of the recent initiatives were prompted by physicistsand feed back into quantum physics.