# Mathematics Colloquia and Seminars

I will describe the structure of nets of local algebras in relativistic conformal QFT with phase boundaries (topological defects) in two space-time dimensions. In the case these boundary is invisible for the chiral net $A\otimes A$ with $A$ a completely rational conformal net on the real line and the nets of local algebras left and right of the boundaries are maximal (modular invariant) local extensions such boundary conditions can be classified.