- October 28th, 2006
- 9:43 pm

In a recent post, pozorvlak reminded me of one of the reason it is important to have a good, obvious, and quick-to-write programming language around.

He, as I, is a mathematician, spending his time thinking, finding patterns, and trying to formulate (more or less) absolute proof that his patterns hold all the time, alternatively ways to demonstrate that they may not be universal.

In the post linked above, he starts by a neat little exercise, gets interested, and goes out to look at more examples. These show a very clear pattern, and after following this pattern quite some way out, he finally believes the pattern enough to start searching for a proof: which he also finds.

This is a preview of

Prototyping thought

.

Read the full post (706 words)
- October 22nd, 2006
- 11:05 am

The term has started. In full force. No seating in the lunch cafeteria, lot’s of people all over the place, lot’s and lot’s of new students, and lectures and examples classes kicking off all over the place.

I’m leading an example class this year: linear algebra and geometry part 1 for the maths majors. One of six different examples class sessions for the same course. And apparently, my good tradition of going out drinking with my students keeps up: I went to the exchange students term-start party last friday, and while partying with the swedes and finns of the scandinavian Stammtisch on the dance floor, a girl squeezes through the crowds past us and asks me in passing if I’m not the examples class teacher. Turns out she registered for my class.

First contact with the students is on tuesday morning.

This is a preview of

Weekly Report: Parties and lectures

.

Read the full post (265 words)
- October 20th, 2006
- 3:15 pm

This blogpost is a running log of my thoughts while reading a couple of papers by Bernhard Keller. I recommend anyone reading this and feeling interest to hit the arXiv and search for his introductions to A_{∞}-algebras. Especially math.RA/9910179 serves as a basis for this post.

If you do enough of a particular brand of homotopy theory, you’ll sooner or later encounter algebras that occur somewhat naturally, but which aren’t necessarily associative as such, but rather only associative up to homotopy. The first obvious example is that of a loop space, viewed as a group: associativity only holds after you impose equivalence between homotopic loops.

This is a preview of

A-infinity and Hochschild cocycles

.

Read the full post (1542 words, 68 images)
- October 18th, 2006
- 3:37 pm

This term, I’m listening to a lecture course on Computational Group Theory. As a good exercise, I plan to implement everything we talk about as Haskell functions as well.

The first lecture was mainly an introduction to the area, ending with a very na

(45 words)

- October 10th, 2006
- 12:22 pm

I just submitted a paper to a journal.

Based on research I have done during my time as a PhD student.

Wish me luck.

*Update:*If you want to read the paper, I suggest you go look at arXiv:math.GR/0610374.

(39 words)

- October 8th, 2006
- 11:08 am

I get the feeling that my pledge to write the weekly reports regularily has been less than successful. So I’ll try to renew that pledge: I shall try to keep up the regularity of my weekly report.

Since last authored, I have been running a mathematics camp for 10th grade kids in mathematics-oriented schools. There are (apparently) 3 or 4 of those in Th

(65 words)