Abstract: Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita–Takesaki modular theory and have many applications to quantum field theory. In this talk, standard subspaces are considered as a subject of interest in their own right (independently of von Neumann algebras). A particular focus are inclusions of standard subspaces, which have similarities to subfactors, and several new methods for investigating the relative symplectic complement of an inclusion will be discussed. A particular class of examples that arises from the fundamental irreducible building block of a conformal field theory on the line is analyzed in detail. Joint work with Ricardo Correa da Silva, see https://link.springer.com/article/10.1007/s00220-025-05458-4. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page