COLUMBIA UNIVERSITY

**Department of
Mathematics
Spring 2009**

**SAMUEL EILENBERG
LECTURES
**

Princeton

**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.**

**- Fri****days
-**

**520 Mathematics - 9:30 a.m.
**

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