Honors College, Class of 2012
Dr. Radu Laza,
Department of Mathematics
Research focus : Interconnections between algebraic geometry, complex analysis, and topology
"It’s really exciting to find out things that nobody has known and that people are also interested in. It’s certainly extremely challenging, one of the most challenging things I have ever done. But it’s a really great feeling when you find something. Whether it’s good or bad, whether you’ve proved something, or found a counter example to something you’ve tried to prove—either way, it’s a really great feeling once you finally find something.
Interview: read more >>
Researchers of the Month: past features
75 features to date!
Be sure to talk to Ken Ascher at URECA's campus–wide poster symposium on April 25th, 2012! And don't miss the talks at the Honors College senior symposium (May 2012, date/time TBA).
Researcher of the Month
If you ever wondered about the interplay between math and music, you'll enjoy seeing how these talents converge in Kenny Ascher, an Honors College senior who has built a formidable repertoire of both math and musical experiences during his undergraduate years at SB. Currently, Kenneth is doing independent mathematics research and preparing to write his senior honors thesis on enumerative geometry, working under the direction of Prof. Radu Laza (Department of Mathematics). While subsequently accruing knowledge of algebraic geometry, complex analysis, and topology largely through independent coursework and research experiences with a variety of mentors (plus graduate level coursework) at SB and across the country, Kenneth Ascher has also simultaneously developed as a jazz trumpeter by playing since freshman year in SB’s Big Band Jazz Ensemble (and smaller jazz ensemble groups) under the direction of Ray Anderson, Director of Jazz Studies.
"Just as jazz musicians take their everyday lives and process them into creative improvised melodies, I have drawn upon all of my mathematical experiences, from my research experiences to my graduate courses and independent studies, to create my own mathematical melody and identity," reflects Ken Ascher who has put a lot of energy into the process of delineating that mathematical identity — fine-tuning his mathematical interests, exploring disparate topics, and assembling a wide array of experiences. As a freshman, undecided initially as to whether to pursue a more applied or pure mathematical focus, Ken sounded out both realms. In summer 2009, he participated in a REU program at Texas A& M where he studied Fourier Analysis and Wavelet Decomposition, using MATLAB applications to distinguish between forged and genuine signatures. In his sophomore year, Kenneth gained valuable research experience in computational biology working in Dr. Robert C. Rizzo's research group (Applied Mathematics & Statistics); that same year, the algebraic geometry class he took with Professor Laza deeply resonated and motivated Ken to pursue his interests in this field. During summer 2010, Ken participated in the REU math program at Texas A&M University, this time working with Professor J. Maurice Rojas in Computational Algebraic Geometry and tackling the study of fewnomial theory and the classical question of when a polynomial has real roots. Follow-up work based on that REU project — finding sharp bounds on the number of expected (non-zero) real roots to univariate polynomials — is currently in preparation for publication; and has provided the foundation for subsequent presentations/honors for Ken: namely, being selected for the Council for Undergraduate Research (CUR) Award at the 2010 MAA Mathfest Conference (Pittsburgh PA) for best presentation on original research, and for an “Outstanding Presentation Award” at the 2011 Joint Math Meetings Poster Session (New Orleans, LA).
This past summer, Kenneth participated in an REU program at Northern Arizona University where he worked with Professor Michael J. Falk to investigate complex hyperplane arrangements, delving into advanced topics within algebra, algebraic topology, combinatorics, and algebraic geometry. When Ken presented “Topology of Graphic Hyperplane Arrangements” this August at the 2011 Young Mathematician's Conference at Ohio State University, he was awarded an Outstanding Presentation Award. Kenneth has also participated in the Garden State Undergraduate Mathematics Conference (1st place, Team Competition 2010; 2011 Poster Session Winner); at the AMS Spring Eastern Sectional (Worcester, MA); and at URECA’s campus-wide symposium.
At SB, Kenneth was awarded the Mathematics Department Junior award (as a sophomore) and is currently taking an independent reading course on Riemann surfaces with Prof. Samuel Grushevsky, in addition to working independently with Prof. Radu Laza for his senior honors thesis. Ken has spent many hours tutoring at the Math Learning Center (Fall 2009-present), and has served as a TA and/or instructor for MAP 103 (Proficiency Algebra) and MAT 123 (Introduction to Calculus). Kenneth graduated from Oceanside High School (Nassau County, NY); and is currently applying to graduate (Ph.D.) programs in mathematics.
Asked about balancing his commitments to math and music, Ken sums up: “I think playing jazz also helps me get away from work for a little while and focus on something else and then go back to the mathematics with a clear mind.” Below are excerpts of his interview with Karen Kernan, URECA Director.
Karen: What is it like doing math research? Do you work alone? Is the work you do collaborative?
Kenneth: It depends. From my experiences, there are some times when I work by myself and then meet with my advisor maybe once a week or a couple times a week to show him what I’ve got: I’d ask him questions, or tell him I’m stuck or that I’ve found something. By contrast, this summer, in an REU program, I worked with another undergraduate on a project. We had very different backgrounds but we were able to put them together to figure things out. I found it was nice to brainstorm with other people and share ideas. Even when I was working in a more solitary way on projects at the Texas A&M REU program, though, once a week we would all meet to discuss our research. We were able to brainstorm ideas with other people, see what other people were doing, and get ideas.
How did you find out about applying to REU programs?
Dr. Alfreda James from the Career Center taught one of the Honors College classes, in my freshman year. Even though I didn’t think I would be eligible initially, she encouraged me to apply. That first year, I sent out applications a little late actually but it worked out. I ended up getting into Texas A&M.
What do you enjoy about doing research in mathematics?
It’s really exciting to find out things that nobody has known and that people are also interested in. It’s certainly extremely challenging, one of the most challenging things I have ever done. But it’s a really great feeling when you find something. Whether it’s good or bad, whether you’ve proved something, or found a counter example to something you’ve tried to prove—either way, it’s a really great feeling once you finally find something.
What is the most challenging thing about doing mathematics research?
One of the really difficult things about math research is sometimes that you don’t know what you’re trying to find. Perhaps in other fields you may have a defined goal. But in math, you start with some assumptions and then just see what you can do from there. You’re not sure always what techniques to use, or even what you’re trying to find. This summer, for instance, we began with one question and then found out quickly that we needed to go in another direction. We ended up finding other things that we wouldn’t have expected.
How has being involved in research helped you develop as a mathematician?
When I came in to Stony Brook, I wasn’t sure entirely whether I wanted to do pure math or applied math. My first research experience here was in computational biology. Then, over the summer (after sophomore year) I did an REU program at Texas A&M which was more pure-math oriented. By doing different research experiences I’ve been able to realize what I do like and what I don’t like to work on. It’s helped me choose what math classes I want to take. Sometimes, instead of taking certain math classes that are offered, I‘ve asked professors to learn other things that aren’t offered by doing independent reading/research classes. Through research, I’ve found out about the topics that I really want to focus on.
Have you had any opportunities to present your work?
Yes, and I’ve really enjoyed these presentation experiences. The best part is sharing your work with other people. It’s also really helpful to share your research with people who know more than you, or have more experience. Maybe they know of a paper to read, or something that can take you in a new direction. I noticed this especially this summer, when I went to one conference, and there was a professor who raised a point that gave me an idea to do something else. While I was responding to a question, and going through an explanation, I was able to think of something new that I hadn’t thought of before. So it can be very helpful, I think, just to get your ideas out, and hear yourself speak about your research—and perhaps realize something you hadn’t thought of before.
What are your long-term plans? Are you going to stay involved in math?
I want to continue doing these things… forever! I want to become a mathematician, be a professor at a university. I’m applying to graduate programs now.
Is there a main focus to your work, to what you want to specialize in when you go to grad school?
I‘m pretty certain at this point that I want to study algebraic geometry or something closely related. For me, taking algebra with Prof. Laza in sophomore year had a big influence, and made me realize that it’s what I want to study. I’m working with him on my senior thesis now.
Is it difficult to describe your work to a non-mathematician?
Some of the research I did at Texas A & M was in a way easier to talk about than say, my current thesis project is because it had lots of applications, whereas the things I’ve been doing more recently—the more theoretical work—is a little harder to communicate.
Do you find yourself getting better and better at communicating math, over time through conference presentations, giving posters, etc.?
Definitely. One thing that has also helped me communicate mathematics better is working at the Math Learning Center. I started there sophomore year. In one week, if you explain the same problem to different people five or six times, it sort of helps you understand it better and to communicate it better. At the URECA poster symposium, I also had the chance to explain my project to people who weren’t necessarily in the field.
What was the best conference experience you’ve had to date?
The Joint Math meeting was fun. It’s extremely large, for one. I think it may be the largest annual math meeting. It was also in New Orleans—so it combined with my interest in jazz. We heard some amazing musicians, just on the street playing music. It was incredible!
Tell me more about your involvement with jazz. Is it hard to balance your two passions for math and jazz?
I’ve been playing in the jazz band ever since freshman year. When I came here as a freshman, I auditioned. And I got in! Practice is three hours a week, and playing on my own time is, optimistically, at least an hour a day or so. And it’s been really great, being able to do jazz here. It’s unlike any experience I’d had in high school It’s a lot more based on improvisation, and expressing your individual self rather than playing in a group. It’s helped me grow as a musician, but I think playing jazz also helps me get away from work for a little while and focus on something else and then go back to mathematics with a clear mind.
Did you choose to come to Stony Brook because of its Math Department?
Yes, I knew it had a very strong math program. And I came in as a math major. I liked how the Honors College was set up (with the education requirements instead of the DECs, plus the opportunity to do an honors thesis) so I wanted to do that. And it worked out that I was able to be involved with jazz too.
What advice would you give to other students?
Definitely do REU programs. They are extremely helpful in exposing you to more math, and understanding what math is like. In a way, the REU programs are supposed to simulate what graduate school is like. So I think that’s a really helpful thing.
Another thing to remember is just that the professors here are really great. They’re all approachable, friendly. Professor Laza, my mentor…he’s extremely patient, as I’ve been learning new things. Professor Grushevsky too has introduced me to great research questions too, and I’ve really enjoyed his classes. Really, all the professors I’ve interacted with here have been really great, in terms of being open: you can go to their offices anytime, ask questions, discuss things. So if you have any interest in a particular subject, just follow up on it, and speak to the professors. The other thing that’s been really helpful is to talk to the other graduate students here. They’re older, have more experience, and are able to share a lot of knowledge and experiences with you.
So you’ve had opportunities to take graduate level classes?
Yes, that’s been really helpful, because in the graduate level classes, a lot of the really great professors expose you to open research problems, to what they’re working on, and what other people are working on. So you really get a sense about what’s going on, and about the research aspect of the field.