**Speaker:** Nils Amend (Bochum)

**Title:** *Supersolvable Restrictions of Reflection Arrangements*

**Abstract:**
Let \(A = (A, V)\) be a complex hyperplane arrangement and let \(L(A)\) denote
its intersection lattice. The arrangement \(A\) is called supersolvable,
provided its lattice \(L(A)\) is supersolvable. For \(X\) in \(L(A)\),
it is known
that the restriction of \(A\) to \(X\) is supersolvable provided \(A\) is.

Suppose that \(W\) is a finite, unitary reflection group acting on the complex vector space \(V\). Let \(A = (A(W), V)\) be its associated hyperplane arrangement. Hoge and Röhrle classified all supersolvable reflection arrangements. Extending this work, we classify all supersolvable restrictions of reflection arrangements to elements in \(L(A)\).

We will discuss this classification with particular respect to the infinite families of irreducible complex reflection groups. This is a report on joint work with Hoge and Röhrle.