University of Oxford

It is well-known that Euclidean domains are PIDs; examples proving that the inclusion is strict are not commonly known. Here is one.

The subgroup growth of finitely generated groups was seen last term, in a lecture of Dan Segal. This time, we see representation growth, and how it is similar to, and different from, subgroup growth.

Brownian Molecular Motors are crucial for cell motility, muscle contraction or any other mechanical task carried out by proteins. After a short introduction to protein motors, I will talk about a numerical appraoch I worked on during the last months, which should enable us to deduct properties for a broad range of protein motors. A special focus should lie on the calculation of the eigenvalue spectrum, which gives insight to motors' stability.

Last week, I proved five theorems about fusion systems, each with a (relatively) trivial proof. All of these theorems were known, but in each case the proof was (in some cases highly) non-trivial. I will introduce fusion systems and talk a bit about why they are interesting, and then prove some, or maybe all, of the theorems I proved.