Make some papers in PhD [closed]

Question

I am a third year PhD Student in math. I am studying abroad from my country. I need some advice.

I have three main problems that I would like to share with you.

1) It seems, I will be graduated with 1 published paper. As you know, finding postdoc position is so difficult even though I would really like to keep doing research in mathematics. Do you have any advice to me for 1 year left of my PhD so that I can get postdoc position easier than now?

2) My supervisor would not like to work with me. Moreover, he is so busy. Whenever I can ask questions from him, he thought about my questions at that moment, not anymore.

I found out I have to work by myself. Unfortunately, I do not have enough experience to work myself and I need to work with someone. I decided to work some mathematician who I met them in some conference. I had some bad experience. Would you please tell me how can I talk to some mathematician so that we make a paper together? In particular, I will meet a great mathematician that I have been following his work since 2017. I made some progress and i would like to show him and convince him to work with me.

3) How much I am good in my field, I am terrible in other branches of mathematics. Let me give an example that show that my question clear. I do high level things in mathematics but I forgot some basic things from other branches that I have learnt several years ago, such as graph, Algebra,number theory,... Is it bad things? What is your advice?

Answer 1

I was in your exact position couple of years back, not that the supervisor didn't want to work with me; rather he left the university and I had no supervision!; and I had to finish up and defend my thesis. So here's my advice to you:

1. Start Your Thesis: You have to start writing your thesis right now! It is a toxic environment when you are 2+ years in and the supervisor is not responsive; and you are still trying to figure things out. So, have a template, and start adding things; and so on. Time is running out and you are responsible for your thesis at the end of the day.

2. Regular Meetings: Send calendar invite to your supervisor for a weekly meeting. If he is not responsive you must inform the head of research group. If you don't you cant say "well my supervisor is unresponsive for the last 4 years and I need to finish my PhD" they will ask you why you didn't inform them sooner.

You might ask: what about papers? Well, you could take part of your unfinished thesis and turn it into a paper. Ideally we want to make papers and write a thesis about it. But when time is running out and you have no direction by the supervisor, you must start writing your thesis, to see what parts of your work need more focus.

That's it! Two important points to finish up your PhD. Finding a postdoc position is not your problem at the moment! You need to finish off your PhD first. Being a Postdoc is not that different from a PhD, what are you going to do if the supervisor is busy again? You need to develop your skills first. So, finish up your thesis and think about defending it, as soon as you can.

Answer 2

It seems to me that none of your problems are especially unusual. They just come together to make it hard to advance.

First, not being very adept outside your specialty is very common. It has been about 100 years since anyone could understand all of mathematics. Extreme specialization is normal. Of course, it is good to retain basic things, but deep knowledge in your specialty is the most important thing for a researcher. My own experience is that mathematical insight is not general, but specific to some small set of fields. For me, Analysis and Topology came fairly naturally, but Algebra was always a struggle.

Second, I think it is also common for students visiting other countries to find difficulties. Especially if there are language or cultural differences, though you don't indicate that as a problem. But your advisor not having enough time for you or being willing to give you some efforts is a serious problem. If you are inexperienced and not finding help it is difficult to advance. My advice would be to try, somehow, to solve the advisor problem, either with this same person or finding another. It might not be too extreme to move to a different university to find the help you need, actually. Expensive and disruptive, of course.

But in today's market, you do probably need some more publications, but that might depend on the quality of the one you have. One way, that you already recognize, is to collaborate and, perhaps, write joint papers. If there is no one at your current university suitable for this then it is much harder, so again, another university might be a better option.

But, as for contacting other mathematicians, you need to ask, but you also need to give them a reason to want to look at your work. This might be hard or not, but it is easier if you are familiar with their work and can make suggestions about how it might be improved and extended. You don't explain the bad experiences you already had with this, of course. But, you could send this new potential collaborator your work and ask for feedback on it. If the feedback is positive, you could ask whether collaboration is possible. But even if it is negative, you can ask if the person can give you some direction for your studies - papers to read, for example.