Much of the advances of representation theory in the 21st century has come from diagrammatic algebra. Though there are often deep ties with very sophisticated geometry, diagrammatic algebra has the benefit of being computationally amenable (depending on your standards) and, as the name suggests, very pictorial. For example, one key diagrammatic innovation this century was the advent of `diagrammatic Soergel calculus', which gives a `categorification' of the `Hecke algebra'. In this course, we will (attempt to) follow the book ``Diagrammatic Algebra'' by Chris Bowman to steal a glimpse into this world.
Students are expected to be familiar with linear algebra, as well as group theory and Modern Algebra I. Some representation theory of finite groups would be helpful.
Each week two students will give talks, 55-60 minutes each. I will assign sections in advance. We will take a short break in between if we decide to do both talks the same day. Students are expected to attend and follow all talks. There will be ``exercises'' each week -- the speakers will each design one exercise, the students will each come up with an exercise themselves, and I will also assign an exercise, for a total of 3. What ``exercise'' here means is nebulous and up to interpretation (probably most often an example computation in a small case). Students may have to give multiple talks throughout the semester, depending on enrollment.