Course Descriptions

16:640:554 - Selected Topics in Algebra

James Lepowsky


Representation theory of vertex operator algebras


None; material will be made available.


Some experience with vertex operator algebra theory would be helpful, but is not required.


Vertex operator algebra theory and the theory of generalized Rogers-Ramanujan partition identities have long been deeply connected.
In fact, the mathematical theory of vertex operators arose out of the problem of trying to ''explain'' the Rogers-Ramanujan identities using representation theory.  Some of the most interesting current research in vertex operator algebra theory is in fact motivated by this same theme.  There is not yet a definitive general theory of what are called twisted modules for intertwining algebras.  Such a theory is
expected to enable the solution of major research problems, which we will discuss in the course.  We will develop concrete examples that illustrate the general theory, and that lead to important unsolved problems and progress toward their solution.

Schedule of Sections: