I will discuss 1-dimensional field theories and twisted 1-dimensional field theories, and indicate how they are related to K-theory. I will then describe 2-dimensional local field theories, sketch a notion of twisted 2-dimensional local field theory, and say how they are conjecturally related to elliptic cohomology. Time permitting I will detail two key ingredients of twisted 2-dimensional local field theory: a good definition of symmetric monoidal 3-categories, and the 3-category of conformal nets. This is joint work with Arthur Bartels and Andre Henriques. |