Your research sounds fun! Is it more math or physics?

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.

While I am sure your successor is smart, that's also the nature of research. (…)

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.

s*) Literally a Navier-Stokes problem.

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.