摘要：I will start with a discussion on the impact of string theory on mathematics. I will argue that string theory demands an entirely a new geometry or new calculus where CFT and D-branes play crucial roles. Then I will introduce a mathematical framework inspired by Segal and the theory of vertex operator algebra to study open-closed CFT. Both the mathematical definitions of CFT and D-brane will be given. In the rational cases, I will show that such open-closed CFTs can be classified. Using this classification, I will discuss some basic properties of the new geometry such as Holographic Principle and a precise relation between dualities and invertible defects.
