Valuations: from convex geometry to function spaces

23/02/2018, 14:00 - 15:00 in MAP/0G/018

Tradacete, Pedro (Universidad Carlos III de Madrid)


Abstract:

A valuation is a function V, defined on a given class of sets, which satisfies that for every A,B

V (A ∪ B) + V (AB)=V (A) + V (B)

whenever both union and intersection of A and B also belong to the class. Valuations are a generalization of the notion of measure, and have become a relevant area of study in convex geometry. I will present some recent results on the structure and representation of valuations on star shaped bodies. These will be based on techniques from measure theory and functional analysis.

Mathematical Sciences Research Centre