|Dept.||The University of Queensland|
Jacobi introduced his theta functions to develop the theory of elliptic functions. Weil's approach to theta functions opened up the way to study them from a representation theoretic point of view. This involves the Heisenberg group, the Stone-von Neumann theorem and the Weil representation of the metaplectic group. I will give an introduction to this topic focusing on the classical transformation properties of theta functions.