In this talk we explore the notion of uniformly distributed (u.d.) sequences.
First we give a measure theoretic definition of this notion on the additive circle $\R/\Z$, and show how this connects with fourier analysis through Weyl's criterion. One realizes that u.d.
sequences are intimately connected to exponential sums, a topic of interest in many areas. Two theorems concerning the quantitative behavior of such sequences will be stated.
These notions could also be extended to more general spaces, in particular we will look at the p-adic unit ball $Z_p$. Although the topic is more than a century old, the speaker believes connections to other areas of mathematics have not been fully explored. Hence, the talk would be of interest to a general audience and perhaps even lead to possible collaborations.