RUI: Randomness, computability, and complexity in groups

Groups are a class of fundamental objects in algebra, and more generally, mathematics. They originated as a way to describe symmetries in both mathematics and nature. It turns out that almost all algebraic mathematical structures can be considered as a group with some extra structure. More recently, group theory has also found uses in cryptography. Many tools from other fields, like combinatorics and geometry, have proven useful in the stud...