How would You encourage graduate students to learn algebraic geometry and/or complex analysis? [closed]

Question

Hello,

I am the 3rd year undegraduate student of mathematics. After I obtain a bachelor degree I want to study maths at graduate level, especially algebraic geometry and complex analysis. This fields of mathematics are well-represented at my univeristy, so at the first glance this plan looks fine.

Unfortunately almost all of my collegues are not interested in this fields (they think that AG and CA are too technically involved; most of them are interested mainly in functional analysis and topology). It will have such unpleasant effect on my studies, that most probably the most (or all) of courses in AG and CA in the upcoming year won't start at my university.

So I'll end up learning alone, from books. It's not that it's a big problem to learn from the book, it's not a problem at all. But I think such learning have no comparison with the regular course, where I could discuss problems and see another approches of other (more gifted) students.

To avoid such situation I may try to convince my collegues to study CA and AG, but I don't have many arguments since I'm still an ignorant in this fields. And here arise my questions:

1. How would You encourage graduate students to learn algebraic geometry?
2. How would You encourage graduate students to learn complex analysis?

Answer 1

This feels really like an "Ask Professor Nescio" question.

Let me ask you a question: if you feel like you cannot learn what you want to learn, why are you staying at the same university? I see from your profile that you are studying a Jagielloni, and you are Polish, so I understand somewhat that, if you want to remain in Poland, you feel that you should stay. But mathematics being the international field as it is, I would recommend going to a different university in a different country. (For example, in the US there seems to be no lack of graduate students who share your interest. I'm sure if you ask around a bit you can find out about other places in Europe.)

Now, with that said, if you decide that you want to stay:

1. Don't over sell it. Being too pushy will have a negative effect on the other students.
2. Don't be evangelical. You should not tell them why they should be interested or why they ought to study the subject with you. That'll have the opposite effect.
3. From your descriptions you need to first dispel the myth that complex analysis and algebraic geometry is too technical. I guess the best thing to do is to introduce them to partial differential equations. (That's a joke.) But you need to be able to show them some examples of how sometimes, things becomes much more clear when viewed in the right framework. Show them a nice theorem or two with relatively simple proofs. A nice forum for this could be an informal seminar organized by the students for themselves: try to run a seminar where each student presents a result (not due to himself) that he finds interesting (don't just hijack it for your ulterior motives). When it is your turn talk about something really pretty from algebraic geometry. It may win you some converts.
4. Find out what your fellow students like to do. You said functional analysis and topology. Anything else? You need to sell to your audience. For the topologists, at least some introductory complex analysis and algebraic geometry should be that hard to sell: tell them about (Hirzebruch-)Riemann-Roch! Tell them about the works of Kodaira! Complex analysis in one-variable is basically just topology anyway. (Can't help you with the functional analysts there.)
5. An extension of the above: convince your fellow students that those subjects are useful for them. So a good idea is to find some theorems in their field that was first proven, or has nice interpretations, using the tools of complex analysis or algebraic geometry.

If all else fail, and you cannot get another person to study with you, you can always ask questions here or on sci.math.