# Chengze Duan: Good position braids to transversal slices of unipotent orbits

**Speaker**: Chengze Duan, UMass

Let G be a reductive group over an algebraically closed field and W be its Weyl group. Using Coxeter elements, Steinberg constructed cross-sections of the adjoint quotient of G which also yield transversal slices of regular unipotent classes. In 2012, He and Lusztig constructed transversal slices of basic unipotent classes using minimal length elements in elliptic conjugacy classes in W. In this talk, we generalize minimal length elements to good position braids in the associated braid monoid of W and use these elements to construct transversal slices of all unipotent classes in G. Moreover, these new elements are also related to affine Springer fibers.