I like studying the zeros of functions. Here's a list of my answers on the topic here on Math.SE. I also enjoy answering questions about asymptotics in general.

Check out my attempt to add real-time previews for comments here on Stack Exchange.

Also take a look at this problem sequence which guides the reader through an application of the saddle point method and derives the equation of the famous Szegő curve.

My avatar is cropped from this image by Garyck Arntzen.