SPEAKER: Ralph Greenberg TITLE: Selmer groups and congruences Abstract: This is the talk that I gave at ICM this summer. I will first introduce Selmer groups for elliptic curves, and then Selmer groups for Galois representations. The main topic of the talk concerns the behavior of Selmer groups for Galois representations with the same residual representation. We describe a variety of situations where this behavior can be studied fruitfully.
