By way of concrete examples, we discuss the dichotomy that in number theory many basic phenomena are either very structured and if not, then they are random. The models for randomness for different problems can be quite unexpected, and understanding and establishing the randomness is often the key issue. Conversely the fact that certain number-theoretic quantities behave randomly is a powerful source for the construction of much sought-after explicit pseudo-random objects.

Light refreshments will be served before the lecture at 3:30 p.m.