Twisting abelian fibrations on hyperkähler manifolds

I will present recent results about twists of abelian fibrations, which is a procedure to build new fibrations out of a fixed one. I will try to outline a general strategy to compute the group of twists in the case of hyperkähler manifolds, and give a modular interpretation of them. Based on a joint work with D. Huybrechts, and another one with Y. Dutta and E. Shinder.