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Every september I coorganize with my friends a “math camp”. The idea is as follows: just before summer holidays we choose a topic we want to learn, we choose a suitable book and everyone of us chooses ~1 of chapters. Then, during 3 months of swimming/skiing/hiking, we become “experts” on chosen chapters. Finally, in september, we meet in Wiselka – small town at the polish seaside (we self-made a big blackboard out of stiff black linen which is very easy to travel with) – and everyone explains their chapters to all the others.
This year we have a serious problem with choosing a topic/book – we have three very interesting propositions and choosing only one is very difficult.
I’ll write here briefly about our previous camps (in case somebody was interested in proved ideas for such a camp) and about propositions for this year’s camp (in case somebody wanted to comment on that, which would be appreciated). Read the rest of this entry »
So I’ve passed my homological algebra exam. Today morning, I unexpectedly realized that I’m going to have a mathematics exam (yes… with the great pain I admit that HA is mathematics :-) and I actually don’t know any proof. This is because HA is so tedious – normally, I feel very uncomfortable if I don’t check at least some details by myself, prove few things by myself, etc. This time, I didn’t check any details. I wanted to several times, but looking at them (I was using a book by Gelfand & Manin) almost always discouraged me.
It’s not that there was nothing that interested me in itself – for example, I really wanted to know why when one passes from category of chains over abelian category to category localized in quasiisomorphisms (see below) then one gets all homotopic morphisms identified. In aforementioned book there are few definitions and diagrams -“nothing is happening”, but I don’t get illuminated even after longer moment of looking at them.
Correspondingly, my knowledge of derived/triangulated categories, simplicial objects and derived functors of nonadditive functors (these were the main topics of a course) is a little bit like a knowledge of history – I know essential facts, I even see some causal connections between them, but I miss something – a spirit of mathematics?.
I’d love to see some comments on how you are/were learning homological algebra. Especially, I’d love to know how (for example) Terrence Tao learned HA (as everybody probably knows, there is non-zero chance of meeting him around wordpress.com, so who knows :-). My General Theory of Geniuses(;-) predicts that he (or maybe He?:-) spent as much time as I did (or less, of course) on the given topic, but his unconsciousness checked all the details and communicated them to his consciousness, one day or another (actually, my GTG says that my unconsiousness also checked all the details, but it saved them for itself, damn bastard.)
Below follows a survey of what I’ve learned on this HA course, part I: derived categories, with some additional thoughts on the subject. I believe you may find it worth reading if you already know some basics of HA (nothing more than classical derived functors) and you’d like to read some informal introduction, to have some view on a matter before studying it for real. Comments are appreciated. Read the rest of this entry »
It’s more than a month since I wrote last post and unfortunately it seems that it’ll take some time ’till I’ll be able to blog again. For last couple of weeks I was back in my home, in Szczecin, and I was supposed to be learning hard. I did not, and accordinly I have to learn hard now (of course, I don’t. I’m f****** wasting my time but I just cannot focus on things when I am forced to).
I already passed PDE exam, now I’m trying to focus on “Complex manifold topology and Hodge theory” and there is still plenty to do about Homological algebra II…….
Oh yes, and the onions… I like them very much, I add them to much of what I eat and accordingly if I’m going to buy myself some onions I don’t buy 3 onions but 5kg so that I have a supply for two months. I put them in refrigerator and it never happens that these onions rot or anything like that.
And yesterday, after I opened my refrigerator for the first time in about 4 weeks (I was back in Szczecin for this long) I discovered that 3 of my precious onions produced green shoots! In refrigerator. For 1.5 month. I was stunned! Almost touched! I just can’t eat them now – this great force of life makes me shed a tear. I moved them out of refrigerator onto windowsill and on monday I’ll buy them some soil and a flowerpot.
The way I see it: there’s a kind of a soul in human body that wants to study hard, learn complex theories, understand why Maxim Kontsevich got a Fields Medal, etc. And there is also resistance of matter – world around that don’t want me to do all these things. Resistance of matter has its agents everywhere.
Few days ago I started to read “The road to reality” by sir Roger Penrose. I didn’t get far yet, but I like one thing about it very much: it’s definetely more than popular science (example: precise definitions of connection and curvature) but it is not academic textbook. The purpose seems to be
giving ideas of contemporary physics and mathematics in as precise as possible_without_pain way. I will write more soon.