US-Canada Planning Visit On the Hurwitz Spaces and Isomonodromy Deformations

美国-加拿大计划访问的Hurwitz空间和ISOMONODROMY形变我们建立了一个国际合作之间的PI，弗拉基米尔Dragovic从得克萨斯大学达拉斯和教授瓦西里萨Shramchenko？来自加拿大Sherbrooke大学，研究了超椭圆曲线的Hurwitz空间、等单点变形、Somos序列该项目将在PI长达十多年的科学计划中开发一个新的方向，即将与椭圆曲线相关的平面Poncelet多边形理论扩展到任意尺寸和超椭圆曲线在这个合资企业中，Hurwitz空间上的微积分技术将在某种程度上变得有效，它们可以用来解决以前无法直接解决的不同领域的问题。关键问题是构建一种新的代数几何方法来求解2x2 Fuchsian系统。该提案的技术内容主要集中在PI，他的博士生和Shramchenko教授之间的科学交流访问;这将包括PI和外国合作者提供的小型课程。该提案的里程碑是将于2015年春季在加拿大舍布鲁克的舍布鲁克大学组织的一次非正式会议研讨会，专门讨论该提案的主题。我们的想法是召集几位来自加拿大的专家讨论相关议题。

US-CANADA PLANNING VISIT ON THE HURWITZ SPACES AND ISOMONODROMY DEFORMATIONSWe establish an international collaboration between PI, Vladimir Dragovic from the University of Texas at Dallas and Prof. Vasilisa Shramchenko ? from the University of Sherbrooke in Canada, to study interrelations between the Hurwitz spaces of the hyperelliptic curves, the isomonodromy deformations, the Somos sequences, and the Pade approximation.The project will develop a new direction in a more than a decade long scientific program of the PI of extending and expanding the theory of planar Poncelet polygons related to the elliptic curves to arbitrary dimensions and to the hyperelliptic curves of any genera.In this joint venture, the calculus techniques on the Hurwitz spaces will be made effective in a way they can be used to attack problems in different fields that before were unapproachable directly. The key problem is a construction of a new algebro-geometric approach to 2x2 Fuchsian systems.The technical content of the proposal is focused on exchanging scientific visits between the PI, his PhD students, and Prof. Shramchenko; this will include mini-courses delivered by the PI and the foreign collaborator. The milestone of the proposal is an informal meeting-workshop which is going to be organized in Spring 2015 at the University of Sherbrooke, in Sherbrooke, Canada, and is devoted to the topic of this proposal. The idea is to gather several experts from Canada to discuss the related topics.