Integrable Systems and Algebraic Geometry

Created as a celebration of mathematical pioneer Emma Previato this comprehensive book highlights the connections between algebraic geometry and integrable systems differential equations mathematical physics and many other areas. The authors many of whom have been at the forefront of research into these topics for the last decades have all been influenced by Previato''s research as her collaborators students or colleagues. The diverse articles in the book demonstrate the wide scope of Previato''s work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts as well as researchers. This first volume covers a wide range of areas related to integrable systems often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties Lax equations integrable hierarchies Hamiltonian flows and difference operators. These powerful tools are applied to spinning top Hitchin Painleve and many other notable special equations.