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I'm a new graduate student majoring in pure mathematics, I prefer topics about geometry and algbra. I have spent three months in this grad school and I found the fact is despressing. There are several main problems.

Firstly, my supervisor is the dean of mathematics, he is very busy and have no time to provide me with guidance. At the same time, my favorite topic is complex geometry. But professors in my department mainly work in algebra and number theory, barely knowing geometry. So I have decided to quit and hope to go to France to study complex geometry.

Secondly, the courses in my school are poor, and what I can choose are abstract algebra ,topology and functional analysis. I knowing the couses are not enough for my futural road so I have two seminars to study differential manifolds and commutative algebra.

What I feel painful and confused are the below questions:

  1. The grades are important for my application in the coming year. But they didn't have much to do with complex geometry, or in other words , I think have learnt the most knowledge I need. I have finished the seminar in differential manifolds, and I hope I could know more about complex geometry and commutative algebra. I think it's hard to do all the things at the same time. How should I allocate my time? Give up some things and try to improve my GPA in order to prove I'm a qualified student to the Application committee？ Or persuade myself this is a challenge I should overcome and try to work hard to get everything done. (Is this really something humans can do?).

  2. My conversation with my mother inadvertently revealed that I thought my partner's level was not so high, and she criticized me seriously. There are only seven algebra students in all grades in my college. After getting to know them, I found that they do not work hard and do not love their major very much. It made me lose some confidence in our seminar. Am I too proud and conceited?

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    $\begingroup$ "At the same time, my favorite topic is complex geometry. But professors in my department mainly work in algebra and number theory, barely knowing geometry." - for your next applications you should spend more time looking at the professor's interests to be sure there are several covering areas you might want to dive into. $\endgroup$ Commented Nov 14, 2024 at 13:25

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I'm going to get slaughtered for this...but I think you need to think MUCH MORE about what you are doing, when moving into academia.

There has been a lot written about it. But I still see generation after generation of new grad students surprised by the problems they encounter--mostly having to do with the poor job prospects afterwards and the massive power imbalence when dealing with their tenured R1 research advisors ("bosses").

Sure...it's kind of a nice experience to not have to (really) work for a living. And you do get an opportunity to study one problem and become a world expert in it (your thesis topic). And it doesn't really take that much money to live, before you have kids.

But you are also throwing some of your most valuable years (in terms of earning potential, physical and mating fitness, etc.) into a holding pattern. And the vast, vast amount of people going that route will not get the tournament prize (R1 tenured professorship).

So, personally...unless you are Lisa Randall quality, my vote would be to bail entirely from academia. The issues with your lacking advisors in your field (the explicit question) are actually smaller than the bigger issues in being in academia (the implicit question). And both your poor planning (in going to a school that lacked your interests) and the school in taking you (as one more of the wasted grad students)...kind of epitomize the general issues with grad students and academia.

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