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

University Of Texas At Dallas, Richardson TX

Investigators

Abstract

US-CANADA PLANNING VISIT ON THE HURWITZ SPACES AND ISOMONODROMY DEFORMATIONS We 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.