Spherical varieties are a generalisation of toric varieties which have a similar combinatorial description in terms of lattice polytopes. I will discuss methods to extend existing classifications of Gorenstein and canonical toric Fano varieties to the more complicated spherical setting. This is based on joint work with Johannes Hofscheier.

In this talk, we will give an introduction to Bredon cohomology, which is an equivariant cohomology theory. We will focus on computations, particularly for the case of the cyclic group of order two.

A polygon is associated to a real toric surface. If the polygon admits some symmetry, then so does the variety. We will see that the quotient of the variety is homotopy equivalent to a wedge sum of circles.