ICTS

Nahm equations are the reduction of the self-dual Yang-Mills equations to one-dimension. By considering the moduli space of solutions to such equations on different intervals and with appropriate boundary conditions, we get a plethora of examples of hyperkahler manifolds. I will review this theory and link it with an interesting conjectural TQFT with values in a category of hyperkahler manifolds. Finally, I will introduce a family of stratified hyperkahler spaces constructed with Nahm equations and whose stratification can be described explicitly using combinatorial data associated to a root system.