This meeting will focus on a special class of lower genera algebraic curves: both hyperellptic and non-hyperelliptic curves that cover elliptic or lower genera hyperelliptic curves. These curves have attracted significant attention because of their appearance in various problems surrounding integrable dynamical systems. These dynamical systems include three celebrated classical problems: Kowalewska's problem of the motion of the non-symmetric top, Clebsch's integrable case of the Kirchhoff problem of body motion in an ideal liquid, and the problem of the motion of 4-dimensional Euler top. The curves relevant to these problems are double cover ramified over four points. Other modern problems include Hitchin's description of non-abelian monopoles, where the cover is non-ramified, the integrable H'enon-Heiles system and its generalizations, where the double covers are ramified over two points, SU(3)-magnet and others. We will discuss the structure of the associated Prym varieties that naturally arise as subvarieties of Jacobians of the curves in question.
The Workshop will be held in the memorial part of Kiev - Podil, at the National University of `Kyiv-Mohyla Academy' .
Brief History of the University
The University traces its origins to 1615, when the noblewoman Galshka Gulevicheva donated land and money to build the Brotherhood Monastery School in Kiev. When Petro Mohyla (circa 1597-1647), the Metropolitan of Kyiv, Galich and all Rus, arrived in Kiev and decided to open a school at Kiev-Pechersk Lavra, the Brotherhood Monastery School appealed to Mohyla not to open a new school but to use the existing institution as the base. Mohyla agreed, and in 1632 the Brotherhood Monastery School was reorganized into the Kiev-Mohyla Collegium, in 1658 it obtained the status of an Academy. Under Mohyla's protection, the monastery and school received additional land and financial support. The aim of the Kyiv-Mohyla Academy was to master the intellectual skills and learning of contemporary Europe and apply them to education in Ukraine. The academy was open to young men from all social strata and attracted students and scholars from Ukraine and other European countries. It flourished at the end of the 17th century and enjoyed its golden age during the reign of Hetman Ivan Mazepa (1687-1709), when enrollment was more than 2,000. The academy's golden age came to an abrupt end with Mazepa's defeat at Poltava in 1709. The ban by Tsar Peter I on Ukrainian publications and religious texts in Ukrainian was a further heavy blow. The school revived for a time after Peter's death, but suffered again under Catherine the Great, whose abolition of the hetmanate in 1764 and secularization of the monasteries in 1786 deprived the academy of its chief sources of financial support. In 1817 the Kyiv-Mohyla Academy was closed down. In 1991, when Ukraine gained its independence, the academy was revived as National University of `Kyiv-Mohyla Academy'.