Abstract: Polyhedral products are natural subspaces of the Cartesian product of spaces, which have a diverse range of applications across mathematics. One particular special case is the moment-angle complex. Work of various authors has identified families of simplicial complexes for which the loop space of their corresponding moment-angle complex is homotopy equivalent to a product of spheres and loops on spheres. In this talk, I will survey the current progress in this direction, and then expand the family of simplicial complexes for which such a decomposition is known - namely simplicial complexes which are the k-skeleton of a flag complex.

Abstract: In this talk I will define Liouville vector fields, Weinstein domains, contact type submanifolds and discuss their connection with Stein structures and rational convexity in $\mathbb C^n$.

Abstract: Mapping class groups of surfaces and handlebody groups are fundamental objects in low-dimensional topology. Quantum algebra and mathematical physics provide large classes of finite dimensional representations for both. In this talk, I will discuss examples of those representations and their properties. An important feature is that they are local under cutting and gluing of handlebodies. I will sketch an approach to a precise formulation of this property and present a complete classification result. The talk is based on joint work with Lukas Woike.