And here’s the final version of my Master’s thesis! Also, a shorter version of my presentation is here: slides, handout, handout (print).

My Master’s thesis colloquium for Mathematics is tomorrow! Abstract:

Abstract. Given tuples of SL2-matrices, one can look at which functions in their coordinate ring do not change when we simultaneously conjugate the matrices: these are called the invariant functions. Our interest in this topic is motivated by the fact that these tuples occur as the so-called “monodromy group” of certain linear differential equations.

We will look at these invariant functions from three different perspectives. First, we employ classical invariant theory to find the structure of the space generated by these invariant functions. Next, we use geometric invariant theory to give a geometric interpretation of this invariant space. Finally, we place the results in the more general setting of representation theory by looking at the structure of the space of matrices as a SL2-representation.

Interesting, huh…

Anyway, some preliminary stuff: presentation, handout and thesis. The final versions will appear later.