Eva Dale 0:01 From the heart of the Ohio State University on the Oval, this is Voices of Excellence from the College of Arts and Sciences, with your host, David Staley. Voices focuses on the innovative work being done by faculty and staff in the College of Arts and Sciences at The Ohio State University. From departments as wide ranging as art, astronomy, chemistry and biochemistry, physics, emergent materials, mathematics and languages, among many others, the college always has something great happening. Join us to find out what's new now. David Staley 0:34 I'm pleased to welcome Roman Holowinsky into the studio today. Dr. Holowinsky is an Associate Professor of Mathematics at The Ohio State University College of the Arts and Sciences. He is also the Managing Director and Co Founder of the Erdős Institute, and prior to that was the Chair and Founding Director of the STEAM Factory. Welcome to Voices, Dr. Holowinsky. Roman Holowinsky 0:55 Thank you very much, David. David Staley 0:56 I'm interested in your research area, and I want to first of all begin by noting that you work in the area of analytic number theory. First of all, for the non mathematicians, tell us what number theory is. Roman Holowinsky 1:07 Number theory is the study of any type of arithmetic or algebraic system for structure, very similar to what we know as the integers 12345, etc. We want to say some very simple things about these arithmetic systems. And primarily, we would like to say things about the fundamental building blocks of these systems. So when we talk about integers, one of the things that we like to ask is like one two, exactly. One of the things that we like to ask questions about are how do we decompose these numbers into their multiplicative fundamental building blocks the prime numbers, so we know that every integer can be uniquely decomposed as a product of primes, 2357, etc. What we would like to figure out with that, is what can we say about the distribution of these primes? Do we know that we have an infinite number of twin primes, primes that differ just by two, for example, we 11 and 13, exactly 1719, etc? Does that difference by to continue on forever? So you can ask very simple questions about these things. And very often, the tools that are required to make any sort of progress on answering these questions can get quite complicated. Now, we can either study this purely through algebraic methods, tools that we happen to have at our disposal through abstract algebra, or we can start trying to break apart these number systems, these fundamental building blocks and insert them into objects that we can apply harmonic analysis to. David Staley 2:49 So, harmonic analysis? Roman Holowinsky 2:51 Harmonic analysis is like calculus on steroids. David Staley 2:53 Oh, okay. Roman Holowinsky 2:54 So why do we want to apply harmonic analysis to these things? Very often, if we are able to prove something non trivial about the analytic objects that we insert these fundamental building blocks into proving something of analytic value, then we end up proving something also non trivial about the underlying fundamental algebraic structure. David Staley 3:18 So, you use the word object, so what does that mean? Are we talking about mathematical objects, are we talking about physical objects. When you say object, what are you referring to? Roman Holowinsky 3:26 I'm talking about L functions, in particular. David Staley 3:29 L functions. Roman Holowinsky 3:29 L functions. The prototypical example is the Riemann zeta function, which is simply the sum of one over one to some power s plus one over two to some power, I suppose one over three dozen power s, etc. This within it also contains the information that the integers can be uniquely factored as a product of primes. So this Darish li series, as we call it, or this L function, also has a representation as a product over primes. And that is because we have the unique factorization of the integers. And studying the Riemann zeta function, trying to prove estimates on this function in terms of how quickly it can grow, how large it can get it in different areas of the complex plane ends up proving non trivial statements about prime numbers. David Staley 4:21 You were talking earlier about twin primes, and what was the highest or the largest. Roman Holowinsky 4:25 Or do we have an infinite series of them, yeah. David Staley 4:28 Do we? Roman Holowinsky 4:29 We believe that we do. This is conjecture, we've made progress as a collection of analytic number theorists, we do certainly have an infinite number of primes with a bounded gap between them a bounded gap, meaning meaning at least we know that we have an infinite number of them that are less than, say 246 apart. I'd have to check with the current record is right now. David Staley 4:53 So, and I suspect you've already taken us down this path; when we talk about analytic number theory, this is applying the two rules that you were describing, that makes an analytic number theory, this is true. So, your research in particular has been looking at classical Delta methods and give us some sense of what this research looks at. Roman Holowinsky 5:12 So delta method is some sort of method in which you're trying to determine that an integer or integer equation is equal to zero. So we could very easily construct some kind of polynomial or some kind of function which has coefficients in the integers. And you would like to know, say this is a function in some variable x, for which values of x is this function equal to zero, being able to detect these kinds of things, is extremely important within analytic number theory for a variety of reasons. One of the problems to which we apply these delta methods is the sub convexity bound for L functions. So again, talking about L functions, in order to establish bounds, we very often have to apply the delta symbol method. And there have been a series of representations for this delta method that people have classically used. And recently, we've been discovering some new variations and simplifications to the classical methods. David Staley 6:17 So, for someone who's not a mathematician, and I wonder if some listeners sort of assume that mathematics is in the end about calculation, but doesn't sound like that's what you're talking about. What's the larger purpose? Why, why be interested in Delta methods or analytic number theory, toward what end? Or maybe there isn't an end. Roman Holowinsky 6:36 Really, I hope that there isn't an end. I mean, we continue to build the field and grow the set of tools and areas of interest as time continues to pass. For me simply, the point is to be able to understand fundamentally, what is the simplest possible tool that I can apply to achieve the end result that I need to achieve? There's this great analogy that was given to me by one of my colleagues, who's currently at Rutgers. And that's to state things in the following manner. We know that we can say crack open a walnut with a massive hammer, and get to what's inside, that is somehow taking a problem and deciding to apply machinery or a tool to it, which is much stronger than is necessary to get the job done. The next kind of level of simplification would be to say, well, maybe I just need a simple Nutcracker, something which is designed specifically for the situation that I have in mind, and I crack the shell open, and I get to what's in the middle. And there's minimal mass and minimal use of force that was put into it, and it's quite elegant. And then somehow, that simplest thing that we could possibly do is to study the walnut as much as possible, understand it in a way that nobody's understood it before. And figure out that all we need to do is simply touch the walnut with a needle pin in one particular spot, and that opens up for us. We give this example a lot in terms of talking about what mathematical beauty might be or what we're trying to achieve, and getting down to the fundamentals of a particular problem. David Staley 8:21 That's interesting. You used the word beauty and elegance; how much do these ideals drive your work as a mathematician? What do those terms mean to a mathematician? Roman Holowinsky 8:30 Well, one of the things I always think about when asked that is even the slogan for the Institute for Advanced Studies in Princeton, it's truth and beauty. For me, at least, when I think about beauty in mathematics, I think about simplicity, I think about what simply feels right, what kinds of insights one needs to make in order to again, establish the ultimate proof that they're trying to establish. Somehow, when you look at things, even outside of mathematics, you can say, that just makes sense, and that's kind of what I try to drive towards, in a proof. If we can get down to the point of simply being, you know what, that makes a lot of sense, then you know, that you're approaching the problem in the right way. David Staley 9:18 You sound as much like an artist, I suppose, as a mathematician, or maybe that's the point, maybe mathematicians are kind of artists. Is that what's happening? Are you engaged in a creative process or a process of discovery, discovering mathematical truths? Are you creating these? Roman Holowinsky 9:33 Well, theoretical math, I mean, epistemologically, we're talking about rational thought. It's not empirical. So for me, I see a lot of connections to the arts and humanities, in particular, how we come about our final results and the direction that we drive ourselves in. It's not generated for me based on data or studies that I'm conducting. It's just based on reasoning. So for me, I absolutely feel a very close tie to the arts and humanities as a theoretical mathematician, sometimes more so than connections to the areas which are more based on laboratory research and gathering of data. David Staley 10:16 And because I've asked this question of artists before, I will ask it of you. So where do your ideas come from, from? Where do they spring? How do they germinate? Roman Holowinsky 10:23 From the shower. I do remember that one time that you ran this program in the Columbus Museum of Art, and we had discussed where individuals find their creative inspiration, I do remember the room being quite divided between those that found inspiration in the shower and those that hated to even think in the shower. Let me answer it in two different ways, ideas for what I might want to work on next, come from engagement with other academics with other analytic number theorists, either through seminar talks, informal conversation online or on the phone, maybe at a conference, or I get inspired by a particular conference talk. Or I'm inspired by something that I've discovered in what I'm currently working on. And I say, you know, that's something that I might want to investigate further down the road. That's where the initial ideas for working on something new come from. But then the actual ideas, which are the ideas that lead to progress on working on a problem can come from anywhere. And I think the longer that you spend time in a research area, the more you start working on your research subconsciously without even knowing it. So very often an idea will come to me, either in the shower, or on a long car journey, when I have time to really step away from all of the other responsibilities and pressures that might be coming at you throughout the regular day. That's where the inspiration comes from. David Staley 12:03 Well, it's the third time used the word inspiration, that obviously plays an important role in your thinking. Roman Holowinsky 12:08 Yes, absolutely. Eva Dale 12:11 Did you know that 23 programs in the Ohio State University College of Arts and Sciences are nationally ranked as top 25 programs, with more than 10 of them in the top 10? That's why we say the College of Arts and Sciences is the intellectual and academic core of the Ohio State University. Learn more about the College at artsand sciences.osu.edu. David Staley 12:36 I noticed that you are currently both the Managing Director and Co-Founder of the Erdős Institute; first off, all tell us about the Erdős Institute. Roman Holowinsky 12:44 The Erdős Institute's primary focus is a multi-university consortium. David Staley 12:50 So, it's a consortium of many universities, is it? Roman Holowinsky 12:52 Correct. Currently, we have Ohio State, Rutgers University and University of Michigan participating in our programming. And the main focus of the Erdős Institute right now is to help graduate students and postdocs with their career placement, in particular with searching for careers that are outside of academia. For me, it's very important to start addressing the problem of the oversaturation of the academic job market. When I was graduating in 2006, with my PhD, I was still lucky enough to obtain my first postdoctoral position that was in the super advanced studies then go on for two years at Toronto as a postdoc. And while I was in Toronto, I ended up proving something that afforded me this position here at Ohio State. But as a mentor now of graduate students, someone who is mentoring multiple PhD students each year, and sometimes multiple PhD students graduating in the same year, I'm starting to personally feel the pressure of being able to help graduate students get successful career placement. And traditionally, in many of the theoretical areas, I think we view the natural career path for someone with a PhD as being a professor. But in the United States, we are graduating over 55,000 PhDs each year, and then we have less than 5000 faculty positions opening up each year. And that ratio is only going to continue to compound year after year. So for me, I started feeling this pressure my other, particularly younger colleagues started feeling this pressure and we all understood that we did not know what the industry job market landscape was like, perhaps in different areas of study and engineering, computer science, etc. You have well established career pipelines with industry. But in many of our theoretical areas in the arts and sciences, we've never considered these kinds of things corporate partnerships or working with industry for industry sponsored research. and so on. So it was something that was very important to me to address on it to make sure that first our students became more aware of what opportunities existed out there for them. And secondly, that we were providing these students with the appropriate supplemental education to get them career ready. David Staley 15:17 What does that mean? What does that education look like? Roman Holowinsky 15:19 So we run seminar series, we run roughly two seminars per month in each university, where we target our grad student alumni that are working in industry, and we invite them to come back and talk to our graduate students about what it is they do in their current role, what it is their company does, and somewhat, most importantly, how they personally got there, post graduation. This establishes that initial peer to peer contact between our graduate students and our graduate alumni. And the students get a sense that here's an individual who was just like me, was able to not take a career path as an academic, and was successful. I can do this too. After establishing that initial peer to peer relationship through those seminar series, we then speak further with these graduate alumni. And we asked them, what skill sets should we be training these students said, After running this now for about three years at Ohio State and having over 40 companies participate in the seminar series, we've greatly learned what additional skill sets we need to be training the students. And then we've been working with these corporations to help create custom tailored boot camps to train a lot of these PhD students with these additional skill sets. One of the hot areas right now for employment for theoretical math, physics, astronomy, or really any of the quantitative, natural mathematical or social sciences is data science, data science, machine learning artificial intelligence. And a lot of companies are eager to hire our graduate students, particularly our PhDs. Even if these PhDs do not have a formal degree that states data science on it. They know that if an individual is able to complete a PhD, then that is a signal that this individual is responsible, is capable of learning on their own, and could be trained in a short period of time in order to be a top employee within their company. David Staley 17:29 So one needn't have a PhD in mathematics. Roman Holowinsky 17:32 That's right, one needn't have a PhD in mathematics. There are certain companies that we speak to that traditionally have hired only theoretical math and physics PhDs, but there are PhDs that have recently graduated from political science that we've placed into these data science positions. David Staley 17:51 You mentioned these 40 or so corporate partners, can you say who some of these companies are? Roman Holowinsky 17:56 Sure. They're all on our websites. Our top corporate participants have been, so far, CoverMyMeds, Root Insurance and Upstart, locally here, and there's also an organization in Philadelphia, a proprietary trading firm, Susquehanna International Group, which has also been a big supporter of our programming, David Staley 18:15 What's the level of their participation in the Erdős Institute? Roman Holowinsky 18:19 So they come in, they give seminar talks, we identify a PhD alumni from respective universities to come in to give a seminar talk, they've given talks at almost all of the participating universities. And then we work with their heads of data science, machine learning artificial intelligence to review the curriculum that we're establishing to make sure that what we're teaching the students would lead to successful employment in the company. And then when we run our boot camps in May, those corporations are on hand to meet with the students to send mentors to send judges on the student projects. And then we also collect data sets from these companies or different challenges from these companies that the students work on, and the students present as a final project presentation day to these corporations. David Staley 19:12 Any placements, any successes? Roman Holowinsky 19:13 Oh absolutely, immediately. So everyone that's gone through the program has been connected to companies that are participating in this program, been hired. The very first success story of was one of my former PhD students. As soon as we started the program in the very first semester of spring of 2017. He then took on an internship at cover my meds over the summer. The company loved the work that he was doing, and he stayed on for a final semester in fall of 2017 to finish up his thesis work, and was then able to work part time at the company while I was doing that work and then started full time employment immediately in the spring afterwards. David Staley 19:55 So there are three universities right now, you say Rutger's, Ohio State, and Michigan: any plans for other university partners? Roman Holowinsky 20:01 Absolutely, we're allowing this to grow naturally. I think it would be most natural to continue to spread this through the Big 10 Academic Alliance. This is a huge talent pool of students to choose from, and it's something that we're hearing from the corporations as well. One of the common laments is that these organizations cannot necessarily compete with the global tech giants and hiring top computer science, PhD talent from the Stanford's and MIT is, and they need to be looking at these other areas, these other disciplines from the state universities, they know there's a lot of talent there. And they know that this is a market, which has not been as tapped as some of these Ivy League type institutions. David Staley 20:48 I note that you founded the STEAM Factory, which I think has attained legendary status now, at Ohio State. Roman Holowinsky 20:55 I hope so. David Staley 20:56 I'm interested in the origins of the STEAM Factory, tell me about its origin story. Roman Holowinsky 20:59 I think the same as with the Erdős Institute, everything is based around community for me. When I first arrived at Ohio State in 2010, we didn't have much in the way of activities are programming for orientation to build academic community among the new faculty that were getting hired into the university. And so a colleague of mine in computer science, Mike bond in 2011, had started a new faculty Meetup group. And that group was just a meeting for very simple activities and formal engagement like happy hours, dinners, concerts, festivals, that sort of thing. And after about a year's worth of time of existence, the group had grown to roughly 40 faculty members that were meeting regularly. And something amazing started happening, the academics started working together. And in hindsight, that makes a lot of sense. Because what else was there to talk about when you're first meeting and other academic other than, you know, what is it that you do? And through these informal conversations and engagements, individuals started establishing research collaborations or teaching collaborations or service collaborations and work was being done in this informal setting after work hours. And we started also hosting various roundtable discussions on things that were of importance to us, like promotion and tenure, or elearning technology. So you know, what are you using? What kinds of software How are you implementing these new hybrid flipped classrooms? Just, you know, we would discuss various things that we thought were important to us also in terms of our professional careers. And so while this group started as a social support mechanism, and kind of a life Information Network, or Angie's List for faculty, by faculty turned into something that was naturally very powerful in terms of generating new collaborative work. And it just so happened, that everything fell together at the right time and right place, we were also acting as a group that would help to give potential new hires tours of the city, we would take them around downtown, or we would take them over to Franklinton to 400 West Ridge for a farmers market or festival. And it just so happened that 400, West Rich was framing off some additional studio space. And that's when the ideas clicked that, you know, maybe what we could do here as a group is formalize get some additional space for us to meet. And since we already were at a size that no restaurant or bar could hold us comfortably and have us all conversing with each other. And something that was a space that was away from work and home kind of a third place for us. And everything just fell into place. And we decided, okay, during winter break between 2012 2013 Let's go ahead and formalize, let's call ourselves the steam factory kind of playing off of the stem to steam movement and education, signalling that we had academics from all different research areas that we valued all the different research areas, and... David Staley 24:14 And factory because 400 West Rich is a former factory. Roman Holowinsky 24:18 400 West Rich was the former EBCO water and sanitation factory. That's right. And in fact, the space that we're in used to be the storage space for all of the broken factory materials. So from the steam factory, both for us to have some kind of office space that we could be working together and gathering together and that would fit the size of our group, but also to start formalizing our outreach engagement and our educational engagement with a broader community by showcasing our research and technology to the public, through the farmers markets and festivals that were happening in that space. David Staley 24:56 What I'm hearing you say is none of this was planned, it was pure inspiration. Roman Holowinsky 25:00 None of this was planned, pure inspiration, everything felt very natural. We went from academic community to academic collaboration, and then the Erdős Institute was the next step of that kind of the commercialization side of things, the external partnerships. David Staley 25:13 And we should be clear, the Erdős Institute sort of grew out of... one of the initiatives of the STEAM Factory. Roman Holowinsky 25:18 Correct, correct. David Staley 25:18 So what's next for your research? Roman Holowinsky 25:21 For my research, I really just allow things to come at me naturally, there are a few things that I would like to get off of my desk that I've been working on for a while. In particular, I am trying to better understand some of these variants and simplifications of the delta symbol method that we've been working on. But really, I just want to see what's going to be the next thing that inspires me either through my next conversation with a colleague or the next conference that I go to. I don't like to plan these things too far out in advance. David Staley 25:55 Roman Holowinsky. Thank you. Roman Holowinsky 25:57 Thank you very much, David. Eva Dale 25:58 Voices from the Arts and Sciences is produced and recorded at The Ohio State University College of Arts and Sciences Technology Services studio. Sound engineering by Paul Kotheimer, Produced by Doug Dangler. I'm Eva Dale. Transcribed by https://otter.ai