The power and beauty of small matrices

We aim to show the importance of the humble sl2, the set of 2 x 2 matrices with trace zero, in Lie theory. Note that no prior knowledge of any Lie theory is required! We will gently build up the world of Lie algebras over complex numbers. In particular, the Jacobson--Morozov theorem is a beautifully simple result showing the eminence of sl2.  

The main theme of the talk is to discuss what happens when the complex numbers are replaced with algebraically closed fields of positive characteristic. This will include recent joint work of the speaker and David Stewart, as well as with Simon Goodwin and Rachel Pengelly. There will be an abundance of concrete examples, calculations with small matrices and even some combinatorics.