## Algebra Seminar

Title: A variant of Artin's primitive root conjecture

Speaker: Kate Petersen

Abstract: Artin conjectured that if b is an integer other than -1 or a square, that b is a primitive root modulo infinitely many primes. Although still unproven, this conjecture is known to be true under the assumption of the generalized Riemann hypothesis. I will discuss the history and some motivation behind studying this conjecture, and survey some known results. Then, I will introduce a generalization of the primitive root conjecture to number fields and discuss some applications to topology and the Euclidean algorithm and present recent progress on this conjecture.