In my talk I will discuss the notion of normalised volume for singularities. For the special case of toric singularities this turns out to be closely related to the notions of Mahler volume and Santaló point in convex geometry. I will explain how well-known facts from convex geometry can be utilised to deduce non-trivial statements about toric singularities. I will also speculate about algebro-geometric interpretations of the well-known Mahler conjecture in convex geometry.
This is joint work with Joaquín Moraga.
