And here's a "general audience" (or "popular math") description of the general theme in this paper, and much of my work in general. Don't hesitate to ask for more details!
In this paper I explore the boundaries of what is mathematically possible when constructing universes of set theory. A "universe of set theory" can be thought of as a model for all of mathematics, and what we, set theorists, like to do, is build different kinds of such universes.
We have two main tools:
1. Take a universe, and add stuff, to create a larger one;
2. Take a universe, and define inside of it a smaller one.
In my paper I use both methods: I extend a given universe and build a larger one, in which I use a specific definition to construct a smaller universe.
The cool thing is, that I can use that definition again - to get an even smaller universe. And again, and again - infinitely many times!