In the theoretical physics community there has been recently an increasing interest towards the analysis and computation of information theoretic quantities in quantum field theory, sparked by their appearence in black hole physics and ultimately by the quest for a quantum theory of gravity. However the quantities studied are often mathematically ill defined and require some kind of renormalization. In this talk, I will review how modular theory of von Neumann algebras provides the tools for the rigorous definition and conceptual understanding of certain entropic quantities, and how their computation can sometimes be performed exploiting the (easier) version of modular theory for standard subspaces of a Hilbert space. I will also point out some connections with problems in elliptic PDEs.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006