The general outline of the problem and the argument was given in the first talk.

In the remaining talks Professor Okounkov will discuss the following topics:

1. the classical Kasteleyn theory of dimers and how it applies to stepped surfaces
2. why discrete holomorphic functions in polygonal domains satisfy additional difference equations
3. how does the additional equation depends on the domain, this is really the theory of noncommutative shifts on the Jacobian, or discrete Painleve equations
4. how to take the continuous limit in part (3)
5. what does this has to do with things like mirror symmetry and other advanced topics for the next year's program