University of Oxford

Presheaves on categories crop up everywhere! In this talk, I'll give a

gentle introduction to 2-categories, and discuss the notion of a

presheaf on a 2-category. In particular, we'll consider which

2-categories such a presheaf might take values in. Only a little

familiarity with the notion of a category will be assumed!

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.