Sean Monahan (Technical University of Munich ) : Horospherical stacks and stacky coloured fans

To begin, I will introduce horospherical varieties and their known combinatorial theory. Horospherical varieties generalize toric varieties and their correspondence with polyhedral fans: instead of a torus action we can use any reductive group, and instead of fans we use a generalization called "coloured" fans. After this, I will highlight some of my research on extending this combinatorial theory to the world of algebraic stacks, namely a correspondence between horospherical stacks and "stacky" coloured fans.