Michi’s blog

Prototyping thought

• October 28th, 2006

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.

Weekly Report: Parties and lectures

• October 22nd, 2006

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.

A-infinity and Hochschild cocycles

• October 20th, 2006

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.

Computational Group Theory in Haskell (1 in a series)

• October 18th, 2006

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 naïve algorithm to generate a permutation group from a set of generators. Next week will bring less naïve algorithms with not quite as horrible complexity.

Before the algorithm can be brought, we’d want some undergrowth: we’d want to be able to work with permutations at all. So, we’ll start with the basic group theory and permutation implementations. A lot of this is stolen or rewritten from this permutation group code.

Our code will make use of two libraries, so if you collate code snippets while reading this, you’ll want to use

If you don’t want to bother with that, the code is available here.

Academic firsts

• October 10th, 2006

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.

Weekly Report: Settling down again

• October 8th, 2006

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 Thüringen, and we had a good portion for each. As a new camp leader, I was very much the odd one out trying to get into the social circles; since kids and leaders alike tend to meet at least two-three times a year for math camps, math competitions et.c. It was fun, though, as expected, and a LOT of alien culture to get into. They do it so very much not like the swedish Unga Forskare.

• FRA-Lagen och falska positiver  9
  Fredrik Reinfilth, Dag, Michi, Dag, Gustaf, Michi [...]
• A vision for collaborative mathematics platforms  7
  Dan Drake, Nathaniel Dean, Michi, Ben Webster, Nathan Dunfield, Joachim Breitner [...]
• AMS and mathjobs.org are made of awesome  2
  Michi, Ben Webster
• Restarting high school topology  1
  John Armstrong
• Tour dates  5
  sigfpe, Charles, John Palmieri, Michi, Charles
• Introduction to Algebraic Geometry (2 in a series)  1
  lhrrwcc

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