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

美国-加拿大计划访问HURWITZ空间和异构变形我们建立了PI，来自达拉斯德克萨斯大学的Vladimir Dragovic和Vasilisa Shramchenko教授之间的国际合作？研究超椭圆曲线的Hurwitz空间、等同构变形、Somos序列和Pade逼近之间的相互关系。将平面庞塞莱多边形与椭圆曲线相关的理论扩展到任意维数和任意属的超椭圆曲线，将为PI长达十多年的科学规划开辟新的方向。在这次合作中，赫尔维茨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。关键问题是构造一个新的求解2x2 Fuchsian系统的代数-几何方法。该提案的技术内容集中在PI、他的博士生和Shramchenko教授之间进行科学访问；这将包括由PI和外国合作者提供的迷你课程。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一次非正式会议-研讨会，专门讨论该提案的主题。这个想法是召集几位来自加拿大的专家来讨论相关的话题。

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.