# Actions of the Quantum Double

#### John Foster

In linear algebra we learn how to write any linear transformation of a finite-dimensional vector space as a matrix. The basic idea of Representation Theory is to study mathematical structures by describing all the ways in which they can be written as collections of matrices. These are called representations. In this talk I will give an overview of the methods I have used recently to find representations of the Hopf algebra and verify their properties.

After graduating from Walla Walla College in 2007, John enrolled in the graduate mathematics program at the University of Oregon. After bicycling several miles to and from school each day of his first year there, he decided that in the event of snow or heavy rain, taking the bus might be a more comfortable option. He is busily preparing his thesis defense for the end of May.