What Is Research?

July 10, 2006

A happy ending?

Filed under: Regular updates,TIFR (VSRP) — vipulnaik @ 8:38 am

Something has clicked of late. Ever since I wrote my last blog post, I’ve been on a high, and no, I didn’t drink. I am here on a mission and am doing it well. And next time, I’m going to do it better.

For those of you who haven’t read the earlier posts, a quick recap. I have just finished my second year of B.Sc. (Hons) in Mathematics (and C.S.) in the Chennai Mathematical Institute. I am really keen on pursuing research in mathematics or allied areas. Currently I am at the Visiting Students’ Research Programme of the School of Mathematics at the Tata Institute of Fundamental Research. The programme started on 15th June and is scheduled to end on 14th July.

My guide here is Professor Dipendra Prasad and I am studying a paper by Bertram Kostant titled Lie Group Representations of Polynomial Rings. The paper is eighty pages, and I honestly don’t think I’ll be able to complete all the eighty pages. Currently, I have understood the first 20-30 pages.

When I first came here, I thought: “I’ll just sit down, start reading, work through the proofs, and keep consolidating my ideas as I go along. Even if I do three pages a day, I’ll finish it in the allotted time.” This is a common trap of reasoning: dividing the “total volume” by the “number of slots” to determine “how much” to do in each slot.

But it doesn’t work that way. For stapling sheets, or delivering milk packets, may be. But for reading a paper, it doesn’t work. For one, there’ll be many days when no progress is made. On other days, what has been learnt previously needs to be consolidated. And most often, as it happened to me, it just doesn’t seem possible to continue reading and understanding the subject.

So the question: how can reading a paper be planned? I’m still wondering. But even as I figure that out for the future, I have in front of me the pressing task of decently wrapping up my tryst with Kostant’s paper on Lie groups.

I am now in the process of finalizing my documentation for the paper. Here’s where I stand roughly: Kostant’s paper discusses three important situations, and gives sufficient criteria for each. I have understood most parts of the proofs of the criteria for all, but there are important gaps. What confuses me most is the way the paper keeps shifting between the “algebraic geometry” approach, the “Lie theory” approach and the usual manipulations with groups and rings (that I’m most confused with). I am often unable to figure out what ingredients are going into a particular proof.

Next, I need to review all the work I have done, and have a short talk ready for presenting to DP (short for Professor Dipendra Prasad) by Thursday-Friday.

After that (which may not happen during the programme here) I need to go through the remainder of the paper which discusses how to figure out whether a given situation satisfies the criteria.

I’ve got to wrap up and prepare for my talk with DP. I’ll post links to my own notes on the papers in my next post.

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