Elliptic algebras and elliptic curves

We give a geometric realisation of elliptic algebras (also
called double-loop algebras) in terms of vector bundles on elliptic curves. We will also discuss the relation to Crawley-Boevey’s recent (half conjectural) solution to the Deligne-Simpson problem of classification of irreducible flat vector bundles on a punctured projective line as well as the relation to the spherical subalgebra of Cherednik’s double affine Hecke algebras of type A.