Department of Mathematics
Spring 2009


Andrei Okounkov

Random Surfaces and Algebraic Curves

Abstract: There exist a number of perhaps surprising connections between certain random surface models of
direct probabilistic interest and seemingly distant geometric questions concerning algebraic curves. On the
one hand, for specific boundary conditions, random surfaces turn out to be counting algebraic curves in some
particular algebraic 3-folds. On the other hand, the probabilistic analysis of such random surface models
requires a different kind of geometric input that may be seen, in some sense, as the "mirror" of the original
enumerative problem. In my lectures, I will try to explain how this works in both directions, introducing the
necessary background material along the way.

- Fridays -

520 Mathematics - 9:30 a.m.
2990 Broadway at 117th Street

Coffee and Tea will be served at 9:00 a.m. 508 Mathematics Building