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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. The articles in this second volume discuss areas
related to algebraic geometry, emphasizing the connections of this
central subject to integrable systems, arithmetic geometry, Riemann
surfaces, coding theory and lattice theory.
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.
This volume contains a collection of papers on algebraic curves and
their applications. While algebraic curves traditionally have
provided a path toward modern algebraic geometry, they also provide
many applications in number theory, computer security and
cryptography, coding theory, differential equations, and more.
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