Posted by Jason Polak on 09. May 2018 · 1 comment · Categories: advice · Tags:

Have you ever thought about what kind of job you can get after your math degree? I’ve compiled a list of the jobs I’ve seen so far in my own search. I’ve divided this post into two sections: academia, most of which require a PhD, and industry, which usually does not require a PhD.

Academia

The research postdoc has a light teaching load that allows you to do research. This is the typical next research academic position you’ll get. Sadly, you might have to go through several of these before you can settle down.
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Posted by Jason Polak on 07. January 2018 · 1 comment · Categories: advice, math · Tags: ,

From browsing my publications, you might notice that my research area changed after my PhD. My thesis was on orbital integrals (Langlands-related), but now I’m working on more classical topics in associative ring theory like separable algebras and Grothendieck groups. In this short article I will explain why I switched areas, in the hope that it will help other young researchers make good decisions.

Let’s go way back to my PhD, in which I solved a problem in the Langlands program. For readers that may not know about Langlands, let’s just vaguely say that it studies generalisations of modular forms through representations of matrix groups and it is motivated by number theory and reciprocity laws. As a graduate student this sounded great because I like number theory and algebra. Writing a thesis was not overly difficult either and I think I did a good job with it.

So, I was excited to get a postdoc in Australia. Besides Australia being an awesome country with cool parrots, it would be a great place to further my research. I even came up with new problems connected to my thesis on which to work. But despite being well set up, I didn’t make much progress. Although I had one paper from my thesis published, when I tried to publish the second part of my thesis, it was rejected multiple times on the grounds that it was not significant enough. From a career perspective, I wasn’t worried because I already had a few other papers (in different areas) either sent out or in progress. But as a young researcher trying to interact with a forbiddingly technical area, it was undeniably discouraging.

Nevertheless, I continued working on more problems in Langlands. In the end however, my interest in the subject began to wane quickly. It mostly wasn’t because of the paper rejection; I’ve actually had one other paper rejected in associative rings and I still happily work on associative rings. It was the fact that although Langlands field is rooted in number theory going back to Gauss, to me it felt completely disconnected from its origins when I was actually ‘doing’ the math. It probably also didn’t help that tremendous amounts of ‘advanced’ algebraic geometry would be necessary for some of the problems I was thinking about, and after giving it a good try, perverse sheaves, stacks, ind-schemes and gerbes were really not to my liking. Hey, I’m happy that some people can enjoy it for what it is, but it turns out it’s not my style.

So I moved onto something else. Actually, one of my many current projects is dimly related to my thesis, but it is far more computational (in fact, it involves writing an actual algorithm in Python) and it is not at all in the style of the traditional Langlands literature. After this project is done however, I don’t plan on continuing in this field. With my new research areas, I am much more satisfied with my work. The only downside is that I now have to find a new community and in particular, new people who are willing to write me letters of recommendation, which has turned out to be much harder than I thought. Still, the switch was absolutely worth it, just because I believe in the math I do again.

There is a lesson in this story, and that is as a young researcher, you should not use a few chosen problems as representative of the general flavour of a research area. Such problems may be interesting on their own, but they are inevitably woven into a highly specialised research microcosm. And the whole research microcosm is something you should consider as well, which includes the general direction of the field and the community and attitude surrounding it. This applies especially to the highly abstract fields that seem to be in vogue these days such as geometric representation theory, Langlands, and higher category theory. In these fields, while a senior researcher can select and distill certain easier problems that would be suitable for many students, only a small fraction of those students will actually have the interest and personality to be successful in progressing to the serious problems of that field on their own. In this regard I’d like to emphasise that it absolutely does take more than just pure brains to succeed. Personality and style is at least as important, and these are things that you may not be fully aware of as a grad student.

So my advice to the young researcher is: know the field you are getting into. Look at some papers in the field and ask yourself if you want to write similar ones. Don’t just be captivated by the ultimate, overarching motivation and instead look at the actual nitty-gritty details of the math and culture. For it is the details you will be spending time with, not the motivation.

Posted by Jason Polak on 05. November 2017 · Write a comment · Categories: advice · Tags: , , ,

I’m getting close to the end of my postdoc and I’m applying for jobs again! So, I thought I’d write some basic guidelines that I found helpful in this process. I will update this guide as time goes by. Feel free to add your own advice in the comments.

Deadlines and reference letters

Most jobs start coming out around September for the following year. After that they keep trickling in all the way until May or even June. The first big set of application deadlines are in November, but some earlier ones are in October. Therefore, you should get your letters well before October. How many letters do you need?

  1. Around 80-90% of academic jobs need three letters. You can feel mostly relieved once you get three.
  2. Some jobs need four letters, and even specify “four or more”. If you can get more than three, which is not always easy, you can pretty much apply anywhere.
  3. Industry jobs usually do not require letters for your initial application but will still require the email addresses of a couple of references.

Almost all academic jobs require at least one letter to mention of your teaching abilities. Graduate students can typically get someone in their department to write this, based on their evaluations from either courses or tutorials.
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Posted by Jason Polak on 19. September 2017 · Write a comment · Categories: advice

Choosing where to get your PhD is an important decision. If you continue onto academia, your PhD might be the longest time you spend at any one institution until you get a permanent position. The most obvious choice is apply to the high-ranking schools. However, you should consider far more than that. Here, we’ll look at some of the important factors to consider, with the context of mathematics in mind. However, most of what I say applies to some other fields as well.

Represented research areas

Unlike choosing an undergraduate program, where the curriculum doesn’t differ much around the world (though it certainly can vary greatly in strength or intensity), a PhD will be on a very specialised topic. So, if you go to a school where analysis and statistics are the main topics represented and you like algebra, you probably won’t like it. This can be worse for those places where you don’t have to choose an advisor until the second year. So I suggest you look at the represented research areas on departmental websites and see what catches your interest. Unfortunately, some math department websites look like they were coded on a Super Nintendo, if that were even possible. So:

Make sure someone is actually doing something you’re interested in at prospective schools!

If you’re at the undergraduate level and not sure of your interests yet, it could be a good idea to consider a masters program first before starting a PhD. I enjoyed doing a masters degree first, even though in the long run it is more expensive.

Total school atmosphere

If you’re lucky enough to be nearby some schools you’re interested in, you should visit them, meet some professors, and even sit in on some classes and departmental seminars. Just walk around and see what it’s like. Some schools have a much nicer atmosphere than others. You should also get a sense of the surrounding city. This is true especially if you are a very independent worker: having an enjoyable city will in fact make working much easier. Conversely, living in a place you dislike for several years is quite draining.

Sadly, living temporarily in cities you don’t like is very probable in at least one stage of climbing the academic ladder.
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