Finally... A Real Task

As usual I have a weekly discussion with my supervisor for the subject on the group theory, topics on Hilbert space and Lebesgue measure. Those three topics are the ultimate goal for the rest of 24/7 days of my life so far. However, for this week, after preparing myself for whole week on my presentation, I didn't managed to present a thing. Since my supervisor has taken the whole time to explain me the general idea of the matter discussed. And I found myself happy with it. I must say that this is the shortest discussion that I've ever had.

Before we end, I suggest few things on my preparation for the comprehensive exam plus continuing on the problems for modern analysis and group theory. He mentioned that in the mean time, he will hand over some journals and group theory problem for me to work on with because later on I may end up working on such problems. Better start now or then.

So I guest this is the beginning of my research work. It doesn't have to wait until I finished all my courses though. But first thing first, I need to pass the comprehensive test. Good luck.

Better Lane for Professional Post

This post is to update everyone that from now on, any post with regards to the label facts and learn will be posted to mylambda.wordpress.com. It provides better platform if one uses LaTeX to write equations.

Ph.D Thesis Proposal

I went to the scariest talk ever this afternoon. The talk was meant for the Ph.D thesis proposal (see below title). This is the first time I've had a chance to joint this kind of a talk. To make this talk even scarier is the audience is a number theorist which make the talk is dense with an unfamiliar notations and terminologies. I think I picked the wrong slots. The topic is not really for me. Well, it is not like I ever want to try to understand the contents but the main idea of joining would be to have some kind of a motivation. I would love to see and feel how's it like to present your thesis proposal because eventually I will do same as this is part of the comprehensive exam. But on the other hand, I do found some familiar concepts like the group homomorphism and irreducible representation being mention in his early talk.

From my observation,

1. There are five audience, which includes the advisor, two co-advisors and two audience (count me in).
2. The advisor and the co are empty handed. No papers at hand and don't even note down a single thing while the speaker is presenting.
3. The speaker used a blackboard for his presentation and not once he ever refer to any reference while he's presenting.
4. The speaker is well known of those of the notations he used, and matters that he was saying.
5. When the speaker get lost or cannot answer some question, his advisor took in charged.
6. When the speaker was not known to an answer, he can definitely say I have no idea...

The thing that I learned would be

1. Be precise (always) what you are explaining. Give examples, perhaps a definition and so on up to every notations that you used. Don't aspect audience is well-aware to what you are presenting even though they really an expert.
2. A general organized talk would be to have a motivations of research, reviews from previous works, thesis problem and expected output.

Note: Apart from the above two things, I need to work on more in the first part. My former supervisor used to remind me of this...

Title of the talk:
Constructing Special Types of Fontaine Sheaves: Comparison Isomorphism Theorems

Favourite Puzzles

The unique thing about every newspaper is the publisher can put up some puzzles just to spice things up for the reader to be acquainted with more than just a news and report scenes. The famous one would be the cross puzzle, match and found the different of two 'alike' but not quite picture and so on. However the best thing in every newspaper in town (Montreal) would be the Sudoku. Yeah... There's always a Sudoku in paper like the Metro (French) and also the Gazzette.

Anywhere in town, especially in the metro subway, one can find people of any age will try to solve out Sudoku. Some are really an old old people. They seem enjoy doing it. Me too, there's even an evil Sudoku to be tried out if one has already being the master and trying to go next level up. Just google into sudoku, tons of related link will be appeared.

The other puzzle that I would like to highlight would be the spider solitaire. hehe... And I just found out that my nice friend Valerie also share the same interest. She played the game once a while in between her research works .

You know, doing theoretical, one need to read a lot and also spending most of his/her time working out the solutions. Which some of them takes longer time then ever just try to work it out. Plus siting in front of the computer for like hours. So when our brain get a little of tired, I especially like to try to solve the spider solitaire. It works to ease the tiredness of the functions of my brain. At least to regain back my energy to continue doing what I've started earlier.

Naive Lie Theory

Naive Lie Theory is an undergraduate text in Mathematics by well-renown Professor John Stillwell, a professor at University San Franscisco, California. I've met Professor Stillwell in 2004 during the TSL Expository Lecture Series III, 2004. Professor Stillwell is one of the invited speaker for the lecture series. I also used one of his famous book, Geometry of Surfaces, 1995 (Springer) during my master research.

Currently I'm using Naive Lie Theory to further upgrade my understanding due to Lie Groups and Lie algebra. As beforehand I'm using a book by Professor Brian C. Hall, "Lie Groups, Lie Algebras and Representations" for my informal reading course with my supervisor. Lie groups (group theory) is one of the tools needed to pursue my future research despite of other methods such as functional analysis, differential geometry and quantum mechanics.

I recommend the reader who have a similar interest as I am to consider the Naive Lie Theory as the next best companion. I like the way Professor Stillwell organized the contents of the book. One must have thankful to be able to find a crash course on groups and their basic important properties.

The book was divided into nine chapters that include, geometry of complex numbers and quarternions, groups, generalized rotation groups, the exponential map, the tangent space, structure of Lie algebras, the matrix logarithm, topology and simply connected Lie groups. Details work are shown in almost of every topics. The best thing is at the end of every chapters there is a discussion that introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.

As catchy as the title, the author used a naive approach that will be usefull to those senior undergraduates or early graduates level as myself.

Note: Some of the exercises is similar as the one Prof. Hall presented in his book. Lie Groups, Lie Algebras and Representations, Graduate Text in Mathematics (GTM), No. 222.

Graduate Student Seminar

Yesterday was the starting of the graduate student seminar for the year of 2009 of the Winter term. Yesterday also, my schedule was pretty tight as I have a replacement of weekly discussion at 2 p.m., then at 3 p.m. my French Cancan session will took place for one hour and half. Later at 5 p.m. I need to rush myself to McGill University for the graduate student seminar for another 90 minutes.

At the beginning I was not plan to go to this seminar which is given by an algebraic (geometric) topologist entitled Introduction to Khovanov homology. Even though the abstract (see below) did mention about the contents will be quite rudimentary. I just knew that, somehow, it was not going to very quite elementary at all. Yes when you are talking about algebraic topology, most of the students here also well-know to the difficulty of the subjects.

However, after finishing my French Cancan session, I decided to go. I don't know where the sudden guts took over me, but I just did. And this time, I'm not going to walk all the way to McGill because I know that I cannot stand the cold and the windchill. So I took the metro instead (so far I have a very close attached to this transport). Still after I went out from the metro (with so many exit doors), I found out I was lost. It's not that the same exit as I was expected to be which is very close and I can see the main entrance of McGill right away. It took me about 10 minutes to figure the way out and I reached the seminar room 15 minutes late and the seminar was already started.

I sit at the very front row (this will prevent oneself to be fall asleep), and telling myself, I'm going to be board and most probably confuse trying to listening to the talk. However... yes however, the speaker was really remarkable. He used an upper case handwriting for the whole time and started to talk mostly algebra and how TQFT (topological quantum field theory) is related to the functors of monoidal map. Mostly he showed the algebra that he used (combinatory) to try to solve some of knot's problem. And he call the algebra and the idea was pretty "cute". How cool is that. I think I never heard anyone telling somethings that is maths were cute. He present it in a leisurely but yet professional and the connection of each topics were smoothly arranged. I admit that I don't recall some or most of the terminologies especially related to knot and combinatory theory, but overall I think it worth to be happened to join this seminar.

Abstract:

About 10 years ago, Khovanov introduced an interesting homological knot invariant. This is a completely combinatorial gadget, that makes use of some interesting algebra. I'll outline the definition, and try to give some highlights of the developments since the relatively recent discovery of the theory. The talk will aim to be quite elementary.
(special thanks go to CRM-ISM website)

Ain's Favourite

My first try: macaronie and cheese

Note: Actually, everyone's favourite