Abel Symposia #5: Differential Equations - Geometry, Symmetries and Integrability: The Abel Symposium 2008

The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

This book contains papers presented at the Abel Symposium 2008, which focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. It presents a modern approach to this classical subject.

I.Anderson, M.Fels: Internal Equivalences for Darboux Integrable.- Ph.Delanoe: Differential Geometric Heuristics for Riemannian Optimal Mass Transportation.- V.V.Goldberg, V.V. Lychagin : On Rank Problems for Planar Webs and Projective Structures.- H.L.Huru: The Polynomial Algebra and Quantizations of Electromagnetic Fields.- N.H.Ibragimov: A Bridge Between Lie Symmetries and Galois Groups.- N.Kamran: Focal Systems for Pfaffian Systems with Characteristics.- P.Kersten, I.S.Krasil: Hamiltonian Structures for General PDE.- B.Kruglikov: Point Classification of 2nd Order ODEs: Tresse Classification Revisited and Beyond.- A.G.Kushner: Classification of Monge-Ampere Equations.- A.Marshakov: On Nonabelian Theories and Abelian Differentials.- R.Moeckel: Shooting for the Eight - A Topological Existence Proof for a Figure-Eight Orbit of the Three-Body Problem.- R.J.Alonso, S.Jimenez, J. Rodriguez: Some Canonical Structures of Cartan Planes in Jet Spaces and Applications.- V.Roubtsov , T.Skrypnyk: Compatible Poisson Brackets, Quadratic Poisson Algebras and Classical r-matrices.- M.Modugno, C.Tejero Prieto: Geometric Aspects of the Quantization of a Rigid Body.- K.Yamaguchi: Contact Geometry of Second Order I