Colloquium
3:00 p.m., Friday (December 16, 2005)
MATX 1100
Ramesh Sreekantan
Tata Institute
Drinfeld Modular Curves and special values of Lfunctions
Most mathematicians at some point or another have come across the equation
\zeta(2)= \sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}
where \zeta is the Riemann zeta function. At first it seems like
a numerical curiosity, but it turns out to have a deeper meaning 
it can be `explained' in terms of certain algebraic invariants of
the rational number field.
Beilinson, building on the work of several people before him,
formulated conjectures which attempt to explain integer values of
the zeta function and its generalization to Lfunctions of
algebraic varieties over number fields. However, these conjectures
have been proved in only a handful of cases.
In this talk we will describe these conjectures and some
generalization of these conjectures to varieties over the function
field over a finite field as well as describe some of the cases
where they have been resolved  in particular, for some
Lfunctions arising from Drinfeld modular curves.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).
