Free growth, free counting

Abstract: I will discuss some recent forays into some counting problems for free objects. I will focus on free inverse semigroups and free regular ∗-semigroups. I will first discuss recent results giving a precise rate of exponential growth of the free inverse monoid of arbitrary (finite) rank, which turns out to be given by a surprisingly complicated but algebraic number. I will then discuss a useful tool for counting algebraic things – rewriting systems – and an elegant bijection which proves a surprising result about the rate of growth of the monogenic free regular ∗-semigroup. Then, and again using the theory of rewriting systems, I will discuss just how non-finitely presented some of these free objects are, and some homological corollaries.

This is joint (in part) with M. Kambites, N. Szakács, and R. Webb.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( slides )

---

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

---