Brunnian links of 3-balls in S^4

In 2019, Budney and Gabai introduced barbell diffeomorphisms and used them to construct knotted 3-balls in S^4. We will review the construction of barbell diffeomorphisms, and show how to use them to construct n-component Brunnian links of 3-balls in S^4 for all n \geq 2. Time permitting, we will mention more applications of barbells towards constructing knotting and linking in S^4. This is joint work with Seungwon Kim and Gheehyun Nahm.