# Partitions, Pentagons and Patterns (Mathematics Colloquium)

Wednesday, October 16 4:10 - 5:00 pm Swart 217

A partition of a number is a non-increasing sequence of positive integers that add up to it. So, for example, 4+2+1 and 4+1+1+1 are partitions of 7. It turns out that 4 has 5 partitions, 9 has 30 partitions, 14 has 135 partitions, and Ramanujan proved the following beautiful result: the number of partitions of 5n + 4 is divisible by 5 for any nonnegative integer n. The study of partitions generates a multitude of deep connections to topics in geometry, group theory, analysis, and other fields of mathematics. In this talk, I will explore some of these connections and show how to prove partition results similar to those of Ramanujan.