Slicing the stars

Abstract: 

How many algebraic numbers are there? Easy: infinitely many. But if we bound their degree and height, we get an interesting counting problem. Answering it involves counting lattice points in certain “star bodies” in Euclidean space. We’ll explain how to asymptotically count algebraic numbers, integers, units and more by approximating volumes of slices of these star bodies, which turn out to possess a remarkable degree of self-similarity. There will be pictures. (This is joint work with Robert Grizzard.)