## Columbia Mathematics Department Colloquium

*"Monodromy"*

### by

### Frans Oort

### (Utrecht
and Columbia)

Abstract:

Where is the terminology "monodromy" used
for the first time in history? We will discuss historical roots of this topic
in the 19-th century and compare these

with work on monodromy
in the 20-th century. Then we will
see how the use of a differential equation enables us to compute a class number

(a
beautiful proof by Igusa, later generalized in various
disguises). We will see how Honda-Tate theory (the topic of our Friday graduate
seminar)

gives a
computation of a monodromy group (as shown by Ribet). And I will conclude by describing joint work with Ching-Li Chai,where
we compute

l-adic
and p-adic monodromy
on certain subvarieties
of the moduli space of abelian
varieties (which connects with my Eilenberg lectures
on Fridays).

.

**October 8th,
Wednesday, 5:00-6:00 pm**

**Mathematics 520**

**Tea will be served at 4:30pm**