First week in PhD

I just officially started my PhD last week, but I already started 3 weeks ago. Here are some of the topics and cool facts I have been reading:

Frobenius Algebra (strongly separable condition, knowledgeable Frob. algebra)

Sheaf: not much apart from allowing me to make some jokes.

Geometric group theory

• Fix k. Let G be a finitely-generated group. There are finitely many subgroups index k.
• Every subgroup of finite index of a finitely-generated group is finitely generated.
• Let G be a free group of finite rank. Then a normal subgroup of G is of finite index if and only if it is finitely generated.
• Table-Tennis lemma: more jokes for me.
• Kurosh's theorem

Reidemeister-Schreier method:  I use this to prove the first point

1. Fix k. Let G be a finitely-generated group. Let H be a subgroup of index k. Then there exists a system of representatives such that the length of each representative is not exceeding k.
2. Let G be a finitely-presented group. Then every finite index subgroup is finitely presented. 

Absurd-but-cute Ideas

I found this article on one of the NY Times blog. It has some of very cute ideas. All were designed by Steven M. Johnson. These are some that I like:

1 Ideas for recreational cars

In particular, I like the number 33.

2. Bicycle vest

3. Nothing to say about this one.

4. Human-powered rail: very similar idea to what I have in my previous post. 

Sharing News

The Brumby Government has finally committed to Melbourne's first bicycle sharing program in its CBD (The Sunday Age). OK, this usually means he will do nothing and pretend that he never said such thing if asked in the future as to why he didn't do anything about it. What fascinates me was the fact that Brisbane will beat Melbourne to the first program in Australia. It signed a contract with JCDecaux with 2,000 bikes and 150 stations by March 2010. Now, compare this with Melbourne's counterpart: 6,00 bikes. That said a lot about the Brumby Government commitment to alternative transportation. So, what is so interesting?

SKM (the company that rejected my application - and my friend's - in 2008) recommended that the speed limit in CBD should be 30km/h. Now if the government eventually gets off its arse, and follows that recommendation, then that would be the real good news. The day might finally come when overtaking cyclists using car in CBD are rare occasions.

On the final note, RMIT industrial design students (shame on you, Melbourne University) decided to take initiative and set up a pilot program called CommonBike. The program will be a bicycle sharing program. The aim is to inform the general public about future bicycle-sharing program, with a side benefit being data collection. Several hubs will be set up around CBD, northern and northeastern inner suburbs. Hopefully, this program will be successful.

Clothes of size S shortage

As much as I would like to claim that I am indifferent to opinions of others, but that is not the case. With this, I realised that I only have  one jumper that I don't mind wearing to university. That generally translate to; I don't wash my jumper for a long time. So recently, I was on a search for my next jumper. 

How hard is it to find a decent jumper that fit me? Very hard indeed. Ok, my size is S and occasionally M, but I noticed that size M is getting larger and larger. Similarly, size S seems slightly too big for me now too. That is beside the point. As a thrifty boy, I don't want to pay more than $30 for my jumper. So, I went on a bargain at different sale. What I found was that there simply no (next to nothing) size S jumper. Similarly, size M was hard to come by. When they came, generally, they were bad designs. All I found were sizes XXL, XL and L. It seems that Melburnians have been "upsize", even during the recession. 

On the other hand, it could be that everyone has already taken most of size S and M. So, there weren't many left to sell. However, that begs another question: If most people wears size S or M, then why the manufacturers keep producing too much L, XL and XXL. Further, it is reasonable to assume that human population size follows - to certain degree - a normal distribution. So, why don't I see more XS and XXS in the shops?

Anyone with answer, please tell me.