$L$-equivalence for hyperkähler manifolds
Two varieties are called $L$-equivalent if the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line. Kuznetsov-Shinder conjectured that simply connected derived equivalent varieties must be $L$-equivalent. I will present examples of hyperkähler manifolds that are derived equivalent but not $L$-equivalent, giving counterexamples to the conjecture.