Right now I got a stack of publications, notes and few book recommendations to get myself started, actual topic is going to be set around mid-November. What really surprised me was the fact that quite a lot of the papers were not on homotopy theory, but non-commutative geometry! In adviser's own words "If you're half as smart as I have been told, you'll probably tell me yourself after reading this"… which I'm choosing to take as someone overselling me as even after going through 20% of material (per volume :P) I feel mainly confused about all this.
Either way, guy is a mathematical physicist so it could end up being pure maths with a few links to physical theories.
Well, good point. But maybe allow me to explain how my former adviser took me from basic problem to something quite complex. I think that my brother once told on IRC about a lecturer who was famous for making similar problem sets for students as homework. Something like:
a) You have a rectangular pool 5 by 5, deep enough to forget about anything other than surface. Solve wave equation for that one.
b) There is a set of pipes, in-flow on the up and drain on the bottom. Using continuity equation find (some parameters, I never had fluid dynamics :P)
r) For a viscous fluid in the potential field of (V, S) where dS is the boundary of the fluid, find a relation between stream, relative distance and speed for a compressible fluid in (some more parameters, you know the idea) that conserves smooth solutions.
Not same person, but the same institute and it seems that that's how they roll. ;)
For about first seven months I was guided from some dumb combinatorics problems about cakes, table seats and multiple dogs climbing on chairs to basically formulating Square-lattice Ising Model on my own (yes, still in the language of previous problems :P). This was when my actual assignment started and was about trying to find when it (the Ising's model solution) breaks and looking for something more general.
Now here's the thing: someone who already had some exposure to at least freshman mathematics should be able to find at least some of them alone. Someone who five minutes ago didn't know what's a Pochhammer's symbol shouldn't be the one who simplifies my solution like it's 2/4 = 1/2 or retraces my steps of the fly asks same questions that took me days to conclude. Maybe I'm that good with explaining stuff. ;)
Either way, thanks for food for thought.