What Is Research?

July 8, 2006

Progress slows down again…

Filed under: Uncategorized — vipulnaik @ 12:46 am

I kept pondering and trying to read up and learn along the directions DP had suggested. But the problem was: I couldn’t get the richness inside my head. And I didn’t have a reliable source from where I could get all the information that was needed for the paper without getting swamped with detail.

I located online Lectures on Invariant Theory and started reading them. But again, progress was slow. Most of the things they talked about were not very closely related to the paper of Kostant, and reading this one, I started getting sidetracked. So I once again started spending my time catching up with other activities, while making more half hearted attempts at getting the flavour of the paper.

As twelve days on the paper were coming to a close, I started getting panicky. Almost half the time was up, and I hadn’t mastered even a single important proof! And I hadn’t even understood the statements of half the theorems. And I hadn’t met my guide except that once!

So on the night of Tuesday the 27th, I sat down and resolved to make progress with the paper. Just read it, plod through the proofs, get it going somehow. And that’s when it struck me: go in for blogging it! May be as I blog down my frustrations, things will clarify themselves and I’ll feel motivated to work.

The next day, I decided to mail DP telling him honestly how little progress I had made and asking his advice. Here is a portion of the mail:

Could you tell me what areas of
algebraic geometry to read up and how they play a role in the paper?

I would also like to have some more general advice on how one goes about
reading papers, as well as more specific motivations regarding this
paper. I feel that my progress so far has been
disappointingly slow.

Could we meet some time today afternoon?

I would also like to present my progress on the paper but I’m not
fully prepared for it, so could we meet regarding that some time later
this week?

That same evening, DP called me and talked for some time with me. He asked me what specific doubts I had about the paper. I said that I’m not getting the hang of it. I asked him how exactly algebraic geometry comes into the picture. I tried to explain what I had understood of the paper so far.

I explained what little I had understood of the use of algebraic geometry, but said that it somehow didn’t quite explain it to me. DP looked at me for some time and said that he himself couldn’t formulate an answer to that.

He then said that if I wanted he could study the paper himself in detail. But I said that I would prefer doing the paper myself and presenting my ideas to him. He reiterated that once I’d start cracking the paper, things would start falling in place.

“Invariant theory is an interesting and relatively new area and it is not all that difficult”, he said.

I must do this paper, I told myself. And it is not as if I have been doing it. But so far, I have had a half hearted approach, with it being a kind of formality. Now, I should do it with greater devotion and with love. Even if it weren’t my first love. If I wanted to make progress, I would have to take responsibility for it, own up to my work.

The paper I finally managed to prepare is to be found here.

Looking forward to your comments… I’ll post DP’s in the next post.

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