Academic member
Luc HAINE
Research description
My research is concerned with the following directions:
A completely integrable system in the sense of Liouville is a Hamiltonian system which possesses enough independent conserved quantities. When the motion is bounded, the dynamics is then periodic or quasi-periodic. The discovery of integrable partial differential equations beginning of the 1970's (soliton theory), has connected the whole area with the theory of algebraic curves, abelian varieties and more recently differential Galois theory.
Symplectic geometry was dicovered by Joseph Louis Lagrange, when he got the idea to describe orbital elements of the planets in the solar system not as constants, but as variables, and defined a bracket between two orbital elements. In this area, I study compatible Poisson brackets and the geometry of the moment map. I am also studying the generalization of symplectic geometry to multiple integrals of the calculus of variations.
Google scholar bibliometric data