Old and New Themes in Number Theory

Abstract: Solutions to equations over integers and over the rational numbers have been an intellectual pursuit that goes back to antiquity. The arithmetic of elliptic curves and modern arithmetic geometry provided new problems and new insights intimately related to some basic questions in the above general context of finding rational solutions to equations. In this talk we shall discuss how Iwasawa theory, and especially non-commutative Iwawawa theory provides a systematic tool to attack some deep open problems in this area.

Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge).