the imaginary tiger society

K3 surfaces: The freshmakers

For the last month or so I haven’t gotten anything done at work. I’d lost interest in what I was doing. A part of this is annual, every year I get fed up with my work and want to quit, and every year I come back from summer vacation anxious to start again.

The other two parts are specific to this year; for one I acheived the goals me and my advisor set out at the beginning of the year, thus immediatly killing all motivation I had for working; and I also broke up with my girlfriend, for reasons that on my side were partly caused by working too much.

So I haven’t gotten anything done for about a month, but today I ran into two guys, an algebraist and a differential geometer, when I was walking out of the lab. It turns out they’ve just printed out some articles on K3 surfaces and are thinking about working on those next year. These surfaces fall exactly into the subject of my thesis and I’ve been meaning to take a serious look at them for a few months.

We go into an office and get to talking during a thunderstorm, and pretty much line out a program to work on all next year. For the first time in a month I’m excited about work. I can’t wait to get up in the morning, jog to work, and find some nice looking conjectures to try and crack next year.

Between this and the complete stranger I picked up and fucked every which way in a meadow under the stars last weekend, the summer is finally picking up.

Nijenhuis

Say you have an almost complex manifold. Now calculate the Lie-bracket of two (1,0) tensor fields. What you get is not necessarily a (1,0) tensor, which is what would happen if the almost complex structure was holomorphic.

If you project your Lie-calculations onto the subspace of (0,1) tensors, you get one form of the Nijenuis tensor. Your almost complex structure is integrable if this tensor is zero. It’s not obvious, but this is what lets you define a holomorphic structrue on the manifold.

I’ve never seen explained where the fuck that tensor comes from, instead it’s always presented as something from the gods. It took me two days of staring at walls to figure that out.

Now, if I could figure out a simple connection between the Lie bracket not having (0,1)-components and the d” operator defining a complex I’d be very happy. But I can’t be bothered.

My last couple of days

Best. Monday. Ever.

I was walking home with this girl I like today and told her I wanted to kiss her. We were saying goodbye because she had some courses to teach, so nothing happened.

After she finished teaching, she texted asking if she could come over. She just left. We spent over two hours in each others arms kissing and cuddling.

Which is all really fun and nice, except for her kind-of-but-not-really-oh-it’s-all-so-very-complicated boyfriend in Nantes. This was the first I’d heard of him, but we were hugging at the time and her hair smelled really nice, so I didn’t care.

So basically I feel really good and happy, but I have no idea what just happened.

Dictionary

This French girl has me coloured properly confused.

On one hand I have absolutely no idea how she feels about me. Whenever I think she wants one thing, she does the exact opposite.

On the other I keep having to reach for a dictionary or Wordreference.com while chatting to her on msn. Damn her superior vocabulary.

Oh well. At least life is interesting.

I fucking hate this

I wish I was smarter.

I’m smart enough to think I’d be a complete cunt to complain about shit. But I’m not smart enough to figure out how to feel better about said shit.

So I just keep quiet and feel pissed off in a corner somewhere.

Fuck.

The dark side is shady and cool

Today I realized I have finally crossed over to the dark side.

I was talking to a friend of mine about something our professor did in a marathon three hour lecture (we’re on holiday this week, so there’s nothing holding him back) a couple of hours before. It’s a process called blowing up, which is used in certain kinds of geometry to get rid of nasty bits in the stuff you’re working with.

Think of a balloon. Before any air gets into it, when you’ve just pulled it out, it’s pretty wrinkled and ugly. Then you blow it up, and all the wrinkles get smoothed out and you’ve got a shiny little thing on your hands. This is basically how the blowing up of varieties in algebraic geometry works, hence the name.

The thing is, I get this kind of intuative description, but I need the details to be able to do something with blowups. And to me the details are… unclear at the moment. They’re what I was discussing with my friend.

Neither of us really understood how blowups worked. We’d gotten most of the actual construction, but we need a few hours or days to get the details into the tip of our fingers. However, we did agree that the end result and actual construction were “pretty concrete”.

I used the word “concrete” to describe the abstract process of desingularizing a variety by replacing a part of it with a copy of n-dimensional projective space. Concrete.

Mine is a dark side now.

My two euros

A cash point just informed me that I’m worth two euros. Plus change. I’ve been overrating my value fiftyfold for the last couple of days.

It’s a good thing I finished signing my contract at work today, so I’ll get paid in about two weeks. This wave of uncertainty and very middle-class poverty is soon at an end.

Until then? Well, I discovered a certain slowness in the French banking system this June, which coincidentally is also the last time this happened. It takes them about a day to realize you haven’t got any money and stop giving you more, so I’ll be set until payday.

Man, I’ll be fucking thrilled when my contract kicks in and I won’t have to pull this kind of juvenile shit anymore.

To hell with thinking

I’m getting interested in a girl. Based on some experiments in this area, where I’ve found that the less I think about what I’m doing, the better things work out, I’ve decided to think as little as possible about everything to do with her.

The romantic of the new century is a stoic, disconnected guy. Our motto?