This is my new blog. I’m not sure how often I will get around to posting, but I’ll try to be doing it from time to time.
I work in semigroup theory. Semigroups have not enjoyed the greatest popularity in the mathematical community. For instance the nlab entry for semigroup suggests that many people think it is a form of “centipede mathematics.” (Think how many legs can you cut off a centipede and still have it walk.) My hope is that this blog will enlighten people about the beauty of semigroup theory and convince them that there is more to the subject than they first thought.
The branch of semigroup theory that has been the most fruitful, in my opinion, is finite semigroup theory. Finite semigroups are very naturally connected to finite state automata, leading to the beautiful field of algebraic automata theory. Such diverse illustrious mathematicians as Samuel Eilenberg, John Rhodes and Marcel-Paul Schützenberger have worked on the subject.
I also hope to touch on the representation theory of finite semigroups, which has found useful applications to finite Markov chains in recent years.