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Absolutely, that's part of my job is to continue my research. Of course this differs at different universities but my university stresses teaching and research and service.
I've got a couple projects going, luckily I've been able to keep up a project related to my dissertation with my advisor here at KU,
so we meet regularly and we've been doing some research. We submitted a paper last summer after I took my summer break here
and luckily I have a good group now at the University of Dayton that's in my same research area so we've been kind of meeting regularly and starting projects.
The big thing for math research is you're supposed to publish articles regularly so my job now is to keep my research active, go to research conferences, and keep writing papers.
So math research is pretty simple. Whatever math area that you're in, you have to solve problems, prove theorems; you know whatever that entails,
whatever that looks like. In pure mathematics it'll look much different than in applied mathematics. You solve your set of problems and maybe you have collaborators
and so on and you write up your paper and you submit it to a research journal and there's a referee process.
They decide whether it's mathematically sound, whether it's mathematically important. They may give some feedback and you may have to make some changes and so on
and then they recommend to the editor whether the paper be published or not. This process is shorter or longer depending on the area of mathematics,
depending on the journal. It may take up to a year, year and a half from submitting the article to when it appears in a journal.
There's a lot of pressure there! You have to time it right. You have to choose appropriate projects and start projects that you know you'll be able to make progress
in and submit those papers in a timely fashion and cross your fingers that everything goes well after that. There's a lot you can't control after you submit a paper
but hopefully you've chosen your research field appropriately and you have a lot of fun doing it. I like doing math research, I like solving problems.
To me they're just fun puzzles. Writing up and submitting - that's kind of the tedious part but it's rewarding in the end when you see your name on a publication.
Getting known by the community, I mean if my name is out there on publications and people are aware of my work, then I have more chances
for collaboration and just establishing myself in the topology community. A more immediate benefit is for my job,
I'm required to publish so much for tenure and then promotion. I am required to do this kind of stuff.