## Speaker:

Sunil Chetty

## Institution:

UCI

## Time:

Thursday, October 23, 2008 - 3:00pm

## Location:

RH 306

This talk will discuss developments in the theory of local

arithmetic constants associated to an elliptic curve E over a number field

k, as introduced and studied by Mazur and Rubin. I calculate the

arithmetic constant for places of k where E has bad reduction, giving a

more general setting in which one has a lower bound for the rank of the

p-power Selmer group of E over extensions of k. Also, by comparing the

local arithmetic constants with the local analytic root numbers of E, I

determine a setting in which one can verify a (relative) parity conjecture

for E.