Topology and Geometry of Multiply Connected Wandering Domains

When iterating transcendental (non-polynomial) entire functions, it is possible to have multiply connected Fatou components. The earliest examples of such functions occur as infinite products. In the first part of this talk, I will show how to construct such an infinite product and discuss what we know about the dynamics and geometry of such domains. In the second part, I will discuss a new approach for constructing such functions, along with some applications and open problems. This talk will be accessible to graduate students, and it features joint work with Kirill Lazebnik.