This is the second weekend in a row spent to more or less large part in the office, working with the product structures on cohomology. Reason for this is that I’m getting my share of the department seminars now – I’m to walk us through the Yoneda cohomology product; the cohomology-as-Hom-in-a-derived-category viewpoint; their equivalence to one another as well as to the cup product; and then talk about restriction and corestriction (i.e. what happens to cohomology when we go between kG- and kH-modules for H a subgroup of G)
This is all not really very bad – I really, really, REALLY need to get a solid grip of this myself too. Only; when I started working on it, I thought I had 4 days and not 11 to prepare in – and dove right into it. Maybe a bit too deeply, so when I (monday) found out I didn’t need to get it done THAT quickly, I kinda dropped most of it for the rest of the week. And now, I need to find a decent proof that cup products = Yoneda products. And I just realized that my books don’t really cover it.
I’m back in Jena now. The last week was spent working myself to the brink of unconsciousness trying to grasp homotopical algebra, simplicial objects, model categories and any and all things Alex sent my way. With some 6-8 hours each day spent on lectures and discussions explicitly held to enable me to understand what was going on, I ended up being halfdead from the mental exercise.
In addition, since I was back in Sweden, outside lecture times was spent almost exclusively socializing in one way or another. Meeting friends. Shopping. Watching movies and spex. And then top it off with an endlessly long trip back.
I left Jena going to Stockholm on Saturday. Thus, much of the week past has been spent in preparation for the trip – reading up on homotopical algebra; getting all the paperwork together and getting my things together for the trip.
Along with “Make sure you learn homotopical algebra” and “Get back primed and ready to teach when you come”, I also was instructed by my advisor to get in touch with $MATHEMATICIAN, who currently resides at Mittag-Leffler and whom he knew from earlier. He is, I am told, very good, very knowledgeable and definitely a resource to be tapped if I should have any chance of it whatsoever.
I desperately, sincerely need to get a better cheap travel route to Jena. This trip now took me €150-170 somewhere, but had a travel time of more than 13 hours. There has GOT to be a better way to go.
Right. It’s thursday. And I had some sort of hopes to do my weekly reports on saturdays. Only, last saturday found me back in Nuremburg, in the middle of a marathon party-after-party session with the RPG crowd there.
Last week was very much characterized by getting various conditions for my being allowed to go to Sweden next week, and getting various bits and pieces of general paperwork in order. In addition to that, I held my first lesson – an examples class in Algebra. Right now, we’re doing modules: general definitions and then the structure theorem for finitely generated modules over a PID. I have already noticed for my self what has been painfully obvious from observing bloggers and friends whining about their students – it’s obvious as soon as you set foot in the classroom who knows what’s going on; and these are the only ones who will give you any sort of life indication. I already started despairing about getting reactions from the people not running up to speed – especially since these also don’t bother handing in any kind of work for me to correct either. End result: I have no idea if I’m doing any good for those who need me, and only get responses from those who don’t. The teacher’s lament.