(8:30~9:00am, Tea, Coffee, and Cookie)

In this talk we discuss recent developments on two problems concerning multiplicative groups of  finite  fields Fpn where p is a prime: the discrete logarithm problem and the problem of  finding primitive elements (a generator for the multiplicative group). The  first part of the talk discusses a recent announcement of Joux's heuristically L(1/4) method for discrete logarithms over finite  fields. In the second part we describe a deterministic algorithm for finding a primitive element for the finite field. The algorithm relies on a relation generation technique in Joux's method. Based on a heuristic assumption, the algorithm  finds a primitive element in time polynomial in p and n. It can also be shown unconditionally that in time polynomial in p and n, the algorithm either outputs an element that is provably a generator or declares that it has failed in  finding one.