Abstract: In the first half of this talk I will explain my PhD work regarding the basic model theory (i.e. with respect to categoricity and stability) of the j-function. I will then outline some work in progress with Jonathan Kirby, concerning the construction of a pseudo j-function in analogy with Zilber's pseudo exponential i.e. how do we go about constructing the best possible model-theoretic analogue of an analytic continuation of the
j-function to the real line?