One of the central theorems of classical Lie theory is that
all split Cartan subalgebras of a finite dimensional simple
Lie algebra over an algebraically closed field are conjugate,
a theorem of Chevalley. This result yields the most elegant
proof that the type of the root system of a simple Lie algebra
is its invariant. In infinite dimensional Lie theory
maximal abelian diagonalizable subalgebras (MADs) play the role which
Cartan subalgebras play in the
classical theory. In the talk we address the problem of
conjugacy of MADs in a big class of Lie algebras
called in the literature extended affine Lie
algebras (EALA). To attack this problem we first develop a bridge
which connects the world of MADs in infinite dimensional Lie
algebras and the world of torsors over the Laurent polynomial rings
and then we give explicit classification of torsors in question.