# Mathematics Colloquia and Seminars

The mathematics of conformal field theory means different things to different people. The three most common ways of studying 2d chiral conformal field theories are i) vertex aglebras, ii) nets of operator algebras, and iii) geometric field theories which assign invariants to complex cobordisms. In this talk I will present an extension of the notion of geometric field theory in which the Riemann surfaces' are allowed to have incoming and outgoing boundary overlap. I will also discuss how these surfaces' are used in studying operator algebraic questions in conformal field theory.