The Return of the advisor

Huzaar... finally my advisor returns from the field. I presented him with everything I had done, he didn't seem too upset, so it was ok really. He gave me a few more ideas to think about. I need to try and convert my recently developed "intuition" for the calculating of the coproduct of the Multiple zeta values into some sort of picture, and then hopefully look for Knot patterns. I also need to look for collections of MZVs of higher weight that give a particularly small coproduct. I also want to learn about the Riemann-Roch Theorem. My advisor says that it is not especially relevent to what I am doing but in the paper "Double zeta Values and modular forms" [Herbert Gangl, Masanobu Kaneko, Don Zagier] the rough statement of Theorem 3 reads:

The values \zeta(od,od) of weight k satisfy at least dim S_k linearly independent relations, where S_k denotes the space of cusp forms of weight k on \Gamma_1.

Informally a cusp form is a modular form that vanishes at a cusp, and apparently one calculates the dimension of spaces of cusp forms via the Riemann-Roch theorem. So, it seems to me that the Riemann-Roch theorem is somewhat relevent. Anyway, I would like to know about it as it seems particularly fascinating. It will however require a brush up on differential forms, sections and the exterior algebra. Perhaps I ought to discuss these topics here, just to make sure I do know what is going on with them.

I managed to get up quite early this morning; the fear of being evicted scared me awake and I managed to leave without seeing anyone from the college. I am now in the departmental computer room, so I will stay here sufficiently late so as to avoid seeing anyone. Plus, they can hardly throw me out past midnight: that would be insane.