ST: Dr. Sweeting, you are the recipient of the prestigious 2024 National Science Foundation's Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship, which will support your research program at the Washington University in St. Louis. Could you please tell us about your path towards and through mathematics which has led you to this remarkable achievement?
BS: I would say my path to this point that I'm currently at began when I took Calculus I with Catherine Beneteau at the University of South Florida, and this was, I suppose, back in the spring 2012 semester. So I started out as a business major at the University of South Florida and it was something I thoroughly enjoyed. But I think part of me was looking for I guess more significant academic challenges (not that business wasn’t), but I guess it wasn't of the kind that I was looking for. And I was just happened to stumble across this class, Calculus I, which I decided to take instead of the business calculus course, to fulfill that math requirement for the major. And I just instantly fell in love. I really liked the way Dr. Beneteau explained concepts and it was truly a challenge for me because I hadn't taken pre-calculus at this point.
So just to kind of, you know, learn about limits of these functions, these trigonometric functions that are now being seen in a different light was just really enlightening and really, really, really interesting. And so from that point forward, I kind of had in my mind that I wanted to do something in the sciences.
I switched my major around a few times. I did Chemistry and then I was in Physics. And then I ultimately decided to do math because of the, I mean, to be honest, because of the simplicity of the curriculum. I mean, once you finish your core classes, anything and everything opens up.
And then I went to grad school at the University of Cincinnati, which was one of the programs recommended by another professor at USF, Thomas Bieske. I met a lot of great people at the University of Cincinnati, including my PhD mentor, Leonid Slavin, who was a great influence on my career. I learned a lot underneath him working on Bellman functions in the study of weighted-norm inequalities.
And from there I had my first postdoc at the University of Alabama with Dr. David Cruz-Uribe, where I kind of was provided the forest for the trees, so to speak, and learned more of the classical techniques for studying weighted-norm inequalities and of some very important problems in the field to which the Bellman function method was successfully applied.
From there I had the fortune of meeting Cody Stockdale and his PhD mentor, Brett Wick, and I've worked with Cody. It's been a kind of contemporary collaborative mindset. He's been incredibly confidence inspiring. And then I had the idea to apply for this postdoc during my final year of my first postdoc at the University of Alabama, and Brett was a natural choice [Editor’s Note: the NSF MPS Aspire PRF is awarded to candidates whose research projects are deemed exceptional and original. They then find a host under whose guidance they pursue the project.]
I mean, he's a very accomplished and strong mathematician and he works a lot of different and in an interesting fields. In particular, he employs harmonic analysis in the study of operators in the setting of complex, several complex variables. So it's going to be nice to employ these techniques that I've been learning about to different areas.
So yeah, that's kind of been my trajectory here.
ST: And what would you consider to be most interesting as research in mathematics?
BS: I like, I guess the variety of questions that can be asked and the satisfying solutions that can be found just to be able to provide some resolute answer to a well-formed and precise question.
That's like something you just don't find in other fields, just this precision and this beauty that comes with it. That's certainly the thing I enjoy most about research and mathematics. I'm interested in other areas of science, as a hobbyist, not as a practitioner or anything, but yeah, to see that, I mean, it really stands out.
ST: Of course. With respect to the wider STEM fields, what do you see as the most relevant research directions?
BS: Oh, that's a broad question. So just in all STEM fields, what do I see as the, I suppose I could provide an answer. I like those interdisciplinary fields like machine learning, deep learning, quantum mechanics, these things that are involving many different fields and combining them.
I know quantum mechanics, quantum sensing, this uses extensively ideas from mathematics, from physics, and it has applications in neurology and chemistry and many other fields. So I think these interdisciplinary areas of research are most interesting at the moment or are the trend. And I think that's quite clear with what you see making headlines. I think also machine learning and deep learning as well, to understand the theoretical underpinnings, a lot of mathematics involved. And then I guess for practical purposes and implementation, a lot of computer science and data science and statistics.
And then of course, where these things are applied, where these models are applied, you have like whatever sub field that is being applied and the knowledge from that area being incorporated.
So I think those are some rather exciting areas.
ST: Definitely. In your opinion, what's the most important current challenge in STEM education?
BS: I think my having students realize or just anyone realize for that matter, I guess the career opportunities that exist, the many career opportunities that exist. And also understanding within these areas. So it's not just being a professor. I mean, there are many different kinds of positions out there that are well paying, that are respectable jobs. I guess talking to students or as this pertains to students, I think everyone's looking for what their career would be.
And when they consider this, it's like, what are some questions like consistency, availability of the jobs, like how well they pay and whatnot, and like quality of life you can have with this employment. And I think like, it's not well known that there are jobs out there that fulfill, that check these boxes that aren't, you know, doctor, lawyer, these kinds of good jobs, like finance consultant.
I mean, these are like the ones that are the most well known and a lot of people, a lot of very smart people are going to these fields because they're guaranteed these things. And so I think just making people aware of these alternate career paths that fulfill these requirements is of importance like in STEM education. And then also conveying the importance or at least just providing a general sense of what research, not just research in mathematics, but what academic research entails.
So I think, I mean, we do a pretty good job, like with these science fairs that kids do, hopefully that's something that's still done in schools, but kind of gives kids an idea of the scientific method and what it's like to conduct research.
But I think more could be done. Just really conveying the utility of science knowledge and just the scientific way of thinking because it extends beyond just being able to answer questions, like research questions. It also extends to processing the world around you.
ST: Of course. And kind of on the same topic, what advice would you have for high school students who are interested in STEM?
BS: I would highly advise just asking, like finding mentors. That is the most important thing. I mean, it's finding people who can assist you on your journey and can answer the questions that you might have outside of the material that's being taught. That way, I mean, you can turn this interest and a passion into something more. So I think and that's been what's helped me along the way is just finding very knowledgeable people who are very open to sharing their advice and their experiences. So yeah, that's probably my top advice.
And from a range of career stages, yeah, it's good to find friends who are interested in these same things that you might be like STEM topics. And then also maybe like kind of like peers that are a little further along the way.
Like if you're in high school, maybe seniors or juniors who like if you're a freshman or sophomore who are interested in STEM and then of course, like contacting your like being in touch with a professor. Like I used to always visit my professors at USF, even if I didn't have math things to talk about, just to kind of maintain connection and just to hear about their experience. Like, I used to go to Dr. Burgos's office at USF to ask him about these things and, you know, talk about things beyond just the material that we learn in class.
I like try to make myself available for my students as well. And those who have taken advantage of this, like there is a difference in their trajectory.
ST: Speaking of which, what would you say was or had the most significant influence on you during your formative years?
BS: It's the people I've met, you know, along the way, like the professors who just like everyone had their own style and I've appreciated every single professor's style that I've had. You just kind of take that in along with the material. Of course, I love math. I mean, I wouldn't be doing this if I didn’t. But like the people make the community like the community makes like helps propel or I guess I don't know, like what an eloquent way of saying this.
But yeah, I would have found out the community there wouldn't be I mean, research honestly relies on a community.
ST: Definitely. As we conclude the interview, are there any final thoughts that you would like to share?
BS: I think it's great that you guys are doing this interview process. Mentoring is very important. I think dissemination of passion and interest is very important in addition to the actual knowledge and information. Like you really want to convey, convey passion is a very powerful thing. Like when students see or when people see that other people are interested in something that then it's infectious.
It stimulates interest in them. And so I think like it's important that that be made known and appreciated for its value.
ST: Of course. That concludes the interview. Thank you so much for doing this.
BS: For sure.