US-Belarus Joint Workshop on Representation Varieties; Norman, Oklahoma; December, 1992

俄克拉荷马大学诺曼分校的安迪·R·马吉德博士和白俄罗斯科学院的弗拉基米尔·P·普拉托诺夫博士将举办这次美国-白俄罗斯联合研讨会，主题是“代表性变种”，特别是普拉托诺夫猜想。来自白俄罗斯的四名研究人员和俄克拉荷马大学的四名研究人员将参加1992年夏末在俄克拉荷马大学举行的为期14天的讲习班，以确定共同的科学优先事项，并为未来的联合项目制订具体建议。表示簇或特征簇是几何对象，其点将给定有限生成群的固定大小的复矩阵表示的同构类参数化。这些对象的一个基本问题是确定它们对哪些群都是有限集。普拉托诺夫猜想推测，只有算术型的线性群才会发生这种情况。通过将参与这项研究最深入的白俄罗斯研究人员(包括普拉托诺夫)和深入参与相关代表性多样性理论的美国同行聚集在一起，研讨会应该能够有效地确定该领域未来联合研究的最有前途的方向。这个数学项目通过使美国和东欧的顶尖专家能够将互补的人才结合在一起，并在相互感兴趣和能力很强的领域汇集资源，从而实现了促进科学知识的计划目标。

This U.S.-Belarus Joint Workshop, to be held by Dr. Andy R. Magid of the University of Oklahoma at Norman and Dr. Vladimir P. Platonov of the Belarus Academy of Science, will be on "Representation Varieties," in particular on the Platonov Conjecture. Four researchers from Belarus and four from the University of Oklahoma will participate in a 14 day workshop at the University of Oklahoma in late summer 1992 to identify joint scientific priorities and developing concrete proposals for future joint projects. Representation Varieties, or Character Varieties, are geometric objects whose points parameterize the isomorphism classes of complex matrix representations of a fixed size of a given finitely generated group. One basic question for these objects is to determine for which groups they are all finite sets. The Platonov Conjecture speculates that the only linear groups for which this happens are those of arithmetic type. By bringing together those researchers from Belarus (including Platonov) who have been most deeply involved in this study, and U.S. counterparts who have been deeply involved with related representation variety theory, the workshop should be able to effectively identify the most promising directions for future joint research in the area. This project in mathematics fulfills the program objective of advancing scientific knowledge by enabling leading experts in the United States and Eastern Europe to combine complementary talents and pool resources in areas of strong mutual interest and competence.