CARMA COLLOQUIUM Speaker: Eric Mortenson, School of Mathematics and Physics, The University of Queensland Title: Ramanujan, partitions, and mock theta functions Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 11th Nov 2010 Abstract: We will give a brief overview and of the history of Ramanujan and give samplings of areas such as partitions, partition congruences, ranks, modular forms, and mock theta functions. For example: A partition of a positive number $n$ is a non-increasing sequence of positive integers whose sum is $n$. There are five partitions of the number four: 4, 3+1, 2+2, 2+1+1, 1,1,1,1. If we let $p(n)$ be the number of partitions of $n$, it turns out that $p(5n+4)\equiv \pmod{5}$. How does one explain this? Once the basics and context have been introduced, we will discuss new results with respect to mock theta functions and show how they relate to old and recent results. [Permanent link]