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Check all your email at Gmail (0 Comments)
2007-03-05 18-50 [Life]

Gmail launched a new service: How do I set up Mail Fetcher? This is very great! Now I can check all my mails at berkeley.edu and math.berkeley.edu in Gmail.

A good instruction is already given in the above link. But before you follow this instruction, check if your basic Gmail display language is English. If it's not, you need to set it into English. This can be done by clicking the "setting" menu in the top line.

Now you can follow the above instruction. So I will only give the information for your math.berkeley.edu account. In your username and password, type your own information. And then type mail.math.berkeley.edu in "POP Server". Port number is 995. This number is the most important one. And you must check "Always use a secure connection (SSL) when retrieving mail". Then you can use your math.berkeley.edu account in the gmail interface. If you reply for your mail coming from math.berkeley.edu account, it would be seen as if you sent it through your math.berkeley.edu account.

Passed the French exam (1 Comments)
2007-02-26 16-52 [Math]

To get Ph.D. in UCB math dept, all graduate students have to take and pass two language exams among French, German and Russian. I took French exam ten days ago with two days of intensive (?) preparation and I passed it. Although I do not know either German or Russian at all, I am in favor of German a little more (since Russian alphabets seems too intimidating).

Now I am planning to take my qualifying exam next semester and for that I collected some past qual syllabus of other grad students with the aid of my secretary Google. I have to find three math dept faculty and one outside faculty. The Qual syllabus which I need to make by myself consists of two major topics and one minor topics. Here are my options:

Lie algebras and Lie groups
Kac-Moody algebras
Representation of Finite Groups
algbraic number theory
elliptic curves
Automorphic Forms
complex analysis

To choose what makes me pass the qual easily, or to choose what makes me study a lot : that is the question.

Ignore it! (0 Comments)
2007-02-22 15-40 [Math]

I began to read the book 'Vertex Algebras for Beginners' written by V. Kac for the reading course. Even though the title says that this book is for beginners, the first chapter of this book starts with 'Wightman axioms of a QFT(quantum field theory) ' which I have never studied. It may not be a book for true beginners.

Anyway, I just skipped those parts about QFT. After that, I met some 'super' things like superspace and super Lie algebra which I am not familiar with also. So I complained to the Prof. B that "I am not familiar with those super things" and he answered "Ignore it!". What a word of wisdom!

Since I didn't know anything from the beginning of a book for beginners, he gave me some advice for reading.

Vertex algebras are not generalization of Lie algebras but that of commutative rings. For example, locality is just commutativity. When you study vertex algebras, find something analogous in commutative ring theory.

Thus have I heard.

Which way I ought to go from here? (0 Comments)
2007-02-10 14-08 [Life]

I am currently reading 'Infinite dimensional Lie algebras' written by V. Kac for my reading course. Since I had only two more chapters to read, I asked Prof. B. "What do you recommend for me to read after this?". He didn't give me a direct answer. He just quoted a scene from 'Alice in Wonderland'

Alice: Would you tell me, please, which way I ought to go from here?
The Cat: That depends a good deal on where you want to get to
Alice: I don't much care where.
The Cat: Then it doesn't much matter which way you go.
Alice: ¡¦so long as I get somewhere.
The Cat: Oh, you're sure to do that, if only you walk long enough.

Ubiquity of Dynkin diagrams (0 Comments)
2007-02-02 19-29 [Math]

A different topic for my talk came up to my mind today: Ubiquity of Dynkin diagrams. In some sense, one of the important themes of 20th century mathematics is the Glory of Lie theory. And this is still in progress today.

If you look at a book on Lie algebras, Lie groups, algebraic groups, refleciton groups, or even singularity of algebraic surfaces, you would propably meet the diagrams like

What are they? Why they come up everywhere?
This seems more interesting than the Klein's quartic story.

Many Cheerful Facts (0 Comments)
2007-01-22 22-36 [Math] [UC Berkeley]

This afternoon, I was asked whether I'm interested in giving a talk in Many Cheerful Facts. So I answered yes. I guess the talk would be on the first week in April. The first year grad students are the main target audiences in my mind. Now I have to decide the topic I will talk about.

When I heard of it, the first one in my mind was the marble sculpture in the MSRI which is in Berkeley hills, Klein Quartic Curve.

The equation for this (complex) curve is

$x^3y+y^3z+z^3x=0$

So is there anybody who wants to know about this mathematical art?

Start blogging in English (0 Comments)
2007-01-20 16-57 [Life]

It has been five months since I arrived in Berkeley. I have been managing my original Blog, Bomber0@NeT in Korean. About a week ago, I decided to make my blog system as dual one.

When I speak English, I usually ignore the grammar to keep the speed of my word flow. But If I write something in English, I cannot ignore it completely since it does not dissappear in a seconds. Even if I try to write correctly, you would probably find very strange combination of words in this blog. But I want you to keep in mind that the important thing is not the language itself but the meaning of which it tries to convey. Even if I took the GRE vocabulary exam, I already forgot those good intellectual words completely. So with only very limited number of elementary words in my hands, I have to express more complex ideas than the words itself. Now I feel that I am like a kid who just started to learn how to write.

In this blog, I would talk mainly about my life here, mathematics, Korea, and so on. This blogging has twofold purposes. One is to share my ideas with others who cannot read my fluent korean writing. And the other is to train my english skill by integrating this training with my daily life. Then let's start the new blogging!