620-619 |
Lecturer: Arun Ram, 174 Richard Berry, phone: 8344 6953, email: aram@unimelb.edu.au
Time and Location:
620619 L01/01 Tuesday 3:15pm - 4:15pm Richard Berry-215 1 hour (L=Lecture)
620619 L02/01 Wednesday 11:00am - 12:00pm Richard Berry-215 1 hour (L=Lecture)
620619 P01/01 Thursday 12:00pm - 1:00pm Richard Berry-215 1 hour (P=practical)
Representation Theory is the art of studying complex structures and symmetries by "representing" them as matrices. Viewing the matrices as linear transformations makes the subject into the study of modules. A general representation/module is a large and complex structure like a molecule and is composed of smaller "irreducible components'' which are analogous to atoms. Often, even the "atomic" representations/modules are intricate and the goal of Combinatorial Representation Theory (and this course) is to explore elementary models which allow us to (more) easily determine properties of these representations/modules: size, number of components, splitting and combination rules, and character. The type of models that are the most useful have the flavor of games for children, like legos or erector sets, and yet these models enable one to obtain very explicit information about the fine structure of the corresponding representations, which may have complexities on the order of the microscopic structure of living cells.
I am away for the week of March 2-6. Emily Peter and Peter Tingley will be starting the course and giving the lectures during the first week. The first homework is found here (pdf version) -- due 7 April.
Assessment will be based on two assignments to be handed in during semester (worth 50%) and a final 3-hour exam at the end of semester (worth 50%).
The plaigiarism declaration is available here. The first homework is found here (pdf version) -- due 7 April. The second homework is found here (pdf version) -- due 12 May.