PIMS PDF at the University of Manitoba, Joshua Males: On Slowing Down, and Finding the Road to Arithmetic Geometry.
Ruth A. Situma, Program and Communications Manager
It’s clear from the way Josh communicates, that he has already found his rhythm. A recent transplant to the University of Manitoba, Josh is originally from the UK and spent the last three years in Cologne, Germany. He moved to Winnipeg, Manitoba, in July 2021. After a 2-week quarantine with “a very friendly cat” at the Airbnb where he stayed, he managed to get out and explore the city in August. “The transition to UofM was very easy (and definitely involved a lot less paperwork than in Germany!), and the department was very open and friendly,” he says. Josh has had a bit of a staggered journey. At one point, he questioned the need to complete a Ph.D. and took a “gap year” from academics. An email from his former supervisor made him rethink his career, and in a series of odd twists, he decided to make his way to Germany. Now, three years later, he is settled into a PIMS PDF position in Manitoba.
“I’ve been working from home for the majority of my time so far in Winnipeg, but do get into the department every now and then. Now that the restrictions on coming into the department are much looser than when I first moved, I’m looking forward to getting in more often. Given that I’ve spent the entire time since March 2020 working remotely (aside from a 3-week stint just before I left Germany when we were allowed back in the office), the adjustment here hasn’t been too tough — and cutting back commuting time is always a bonus!” he notes.
Tell us about your field of work and how you got there?
My work mainly focuses on analytic number theory but also reaches combinatorics, topology and arithmetic geometry. How I got here is a bit of a strange journey. Back in 2016, I was finishing up my masters at Durham University in the UK, and was lucky to have Jens Funke supervising my master's thesis on aspects of automorphic forms and L-functions over the rationals. It was Jens who first introduced me to the world of modular forms (and I am very grateful for it!). As I was finishing up the masters, I had only applied to only a handful of places in the UK, so I ended up taking up a sabbatical role at Durham University in the sports department, running the intramural leagues and competitions and competing for the university in the premiership.
I think it is quite normal to need and take a break — and you seem to have come back with some new goals and a vision to work towards. What made you decide to pause for a year in the first place?
I was slightly unsure of going for a Ph.D. in the beginning for a couple of reasons. I had not had so much exposure to research mathematics, especially in my current field, by the time applications were rolling around in my 3rd year of university. The second reason was more for health reasons — I ended up dedicating my Master's thesis to various people who were very close to me that I had lost. That was particularly challenging and I had quite a rough time at university. I also lost a close friend of mine to suicide at the end of my first year and that really took a toll for several years — I ended up feeling fairly lost, and didn’t know what the right path was for me.
I may have taken a position in industry at the time, but knowing what I know now about mathematical research, I definitely think I would have ended up feeling pretty unfulfilled in industry if I wasn’t applying my mathematical skills. Probably I would have ended up in finance or tech as they both have aspects that are appealing to me, but in the end, I just couldn’t get away from the feeling that maths was something I have to do, and I’m very glad I ended up where I am.
You know, in many ways a sabbatical or gap year really depends person-to-person. For some, I know the break is a welcome relief from the pressure we can feel in academia and gives a chance to mentally reset before the tough Ph.D. journey. On the other hand, taking a complete break from maths for a year or more can make it tricky to get back into the swing of thinking mathematically, and the allure of corporate jobs with more stability can definitely keep you away from academia once you’re there. If I had to do it over again though, I would take the sabbatical every time.
You took some time for self-care, and to reflect on your mental health and academic trajectory. What got you back into academics, and eventually connect to your current PDF supervisor, Prof. Siddarth Sankaran?
You know, in many ways the year-long sabbatical was great for me and gave me time to reflect on whether a Ph.D. was really the right route to take. Having decided that it was, I had “another chance” at Ph.D. applications in the next round, having finished the master's thesis and being exposed to modular forms and more research mathematics. I also kept in touch with Jens during the sabbatical (and still keep in touch) and attended a couple of conferences to get to know more about the field. In the end, it’s an email from Jens that also got me moving.
Larry Rolen, a professor in Dublin, emailed my former supervisor Jens, toward the end of 2016. He had a Ph.D. spot available and wondered if Jens knew anyone for the position. Jens, of course then emailed me about it. After being put in touch and talking about research, Larry offered me a spot to join him in Dublin, Ireland the following year. Unfortunately, that ended up not working out as Larry moved back to the US. However, he kindly put me in touch with Prof. Kathrin Bringmann in Cologne, Germany, and she graciously took me in as a student on about one month’s notice!
Oh, wow! Talk about your stars aligning! What was it like working with Prof. Bringmann, in Germany?
Working with Kathrin was an amazing experience, and was a large part of shaping my professional career path. I spent three and a half years working under Kathrin on various aspects of modular forms and was very fortunate to be introduced to some of her research network, as well as enjoy research trips to collaborate with Larry and Ken Ono in the US. Many of my papers focus on the asymptotic behaviour of coefficients of modular forms, a few of those most related to this area are:
Asymptotic equidistribution for partition statistics and topological invariants — submitted (with G. Cesana and W. Craig).
Distributions on partitions arising from Hilbert schemes and hook lengths — submitted (with K. Bringmann, W. Craig, and K. Ono).
Asymptotic equidistribution and convexity for partition ranks — The Ramanujan Journal, 54, pages 397–413 (2021).
I applied to work with Siddarth Sankaran here at the University of Manitoba because of his expertise in arithmetic geometry — an area I had some exposure to during my Ph.D. but would like to study more. Since moving to Winnipeg, I’ve enjoyed complete freedom to choose my projects, have kept working with collaborators in various areas of modular forms, and have built a fairly strong research agenda with some exciting results also in the works.
We’re so glad you get to be a part of PIMS and have found your rhythm. In addition to your research, are you teaching? What is the experience like?
This semester I’m teaching Calculus II, which is all about introducing students to integration techniques and applications. It’s still my first year as an instructor of such large courses so I’m definitely learning a lot, and we are still teaching online at the time of writing. So far I’m really enjoying teaching — the students are diligent and ask great questions, and I find that teaching is also a nice way to be forced to take a break from research once in a while. It will be great to get to experience teaching such a big class in-person once we are able.
What do you do now, to balance your research and life? What does a typical Sunday look like for you?
While I wouldn’t describe myself as a workaholic, I definitely feel like I am some days. Especially working with collaborators from the US, Europe, and Australia, I have to be very flexible with my working hours — 7 am meetings and 7 pm meetings are both pretty common for me. To combat this, I try to head out to play plenty of sports — most of my time away from work is spent playing badminton. I used to train and compete across Europe, but now I tend to just play for fun a bit more. Aside from sports, I love to travel, and I’m going to try to get out and explore various parts of Canada over the summer once the teaching semester is over (I’m especially looking forward to hiking around Banff!).
A typical Sunday doesn’t start too early (I save my energy for that for the weekdays), and I usually head across to the gym at around 10. I’ll spend most of the day there, until around 5 or 6, either playing badminton or swimming. In the evening, I’ll take a look at Monday’s articles on arxiv in number theory and see if anything interesting for my research has been uploaded, and then just catch up on any admin-type tasks I put off a few days before.
What do you miss from your time in Europe and what is your best discovery since arriving in Winnipeg?
My best discovery has to be (at the risk of repeating myself) the gym I’ve joined and the people there — it’s nice to have a place to relax and get away from work. I miss a few things from Germany and Europe. I haven’t managed to see my family since before the pandemic, so they are definitely top of the list. If I could bring anything from Cologne to Winnipeg it would definitely be the (free) public transport, and last but not least the bakeries every two or three shops on the streets!
Joshua Males received his MMath (masters + bachelors) degree from Durham University, UK, under the supervision of Jens Funke, before taking a year sabbatical in Durham. In late 2017 he joined Kathrin Bringmann’s number theory group at the University of Cologne, Germany, where he earned his Ph.D. in May 2021. Since August 2021, Joshua has been a PIMS postdoctoral fellow at the University of Manitoba, working under his mentor Siddarth Sankaran. His research focuses on modular forms and their use in number theory and beyond, with connections to combinatorics, topology, and arithmetic geometry. At the time of writing, Joshua has 8 published articles (4 as solo author) and 6 preprints (1 as solo author) as well as 3 more articles in the latter stages of preparation.
Joshua will be speaking at the PIMS Emergent Research Seminar Series, on March 9, 2022, at 9:30 AM Pacific. Details on his talk, Modular forms, and their role in counting combinatorial and topological objects can be found here.
