Associate Professor of Mathematics Amanda Folsom is originally from Boston. She received her bachelor’s degree in mathematics from the University of Chicago and went on to obtain her master’s degree and doctorate at the University of California, Los Angeles. Folsom specializes in number theory, particularly in modular forms and mock modular forms.
Q: How did you know you wanted to be a mathematics professor?
A: I think, for me, it was a bit of a slow evolution. I tested out different majors in college, like many college students do. I tried out classes in computer science, physics, math and other sciences. I felt like I was always leaning that way, but I wasn’t sure that math was the one until I realized that what I really liked about computer science or physics was the logic and the mathematics behind the scenes. I really fell in love with math after I started taking some excellent courses as an undergraduate at the University of Chicago. I had some amazing professors and eventually majored. But even then, I wasn’t quite sure that I wanted to go to graduate school or that I wanted to be a professor. So, I actually tried out an undergraduate math research program after my junior year. I was curious about what math research was all about: What did math research even mean? And I got the experience to see it firsthand. The rest of it is almost history, at that point. I had an amazing experience and decided to apply to graduate school and went to graduate school. I thought a lot about other things, but around the third or fourth year, my internal reflections came to an end. And I decided that yes, I really love teaching, and I love my research. I wanted to teach at the college level and continue my research, so that’s what happened.
Q: What did you do immediately before you became a professor at Amherst?
A: I was a tenure-track assistant professor at Yale in their department of mathematics for four years. So there, in some ways, my job was similar to what it is here, but in some ways, it was a little different. I also taught a variety of undergraduate courses, but also some graduate courses there. I advised a Ph.D. student who is actually graduating with her Ph.D. from Yale this May. And I actively participated in their number theory research seminar, which we do actually also have here at Amherst — a joint program with the University of Massachusetts Amherst, Mount Holyoke, Smith and Hampshire. So that is something I continued here in a different location.
Q: What do you like best about being here at Amherst?
A: I feel such a warm sense of community here. And I mean that with respect to the students, but also with respect to my other colleagues and the faculty — not only the mathematics department, but across campus. I feel such a sense of community here, and I love that.
Q: What are your specific passions and research interests in your field?
A: I am a number theorist, and in particular, I think about modular forms and related functions. So, what on earth is a modular form? It’s a function that takes on values in a complex plane, like imaginary numbers. Modular forms are functions that have complex values, in the sense of complex numbers. It looks just like when you’re graphing functions in calculus on a plane, right? The complex plane is exactly like that but the way you pinpoint the actual numbers is slightly different. They are a little more special than that in that they obey certain symmetry properties, meaning if you evaluate the function at one complex number, it will equal the value of the function at an infinite number of other complex numbers.
So that all may sound a bit abstract, and in some ways it is. I am very much an abstract mathematician, so I often just think about these functions and their deep properties and structures for their own sake. But I’m also particularly interested in modular forms because you can prove theorems in many different areas using modular forms. For example, if you take the number 5 and I could ask you how many different ways can you partition the number 5. By partition, I mean rewrite 5 as a non-increasing sum of other positive integers. So 5, you could write as 5. You could also write it as 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1 or 1+1+1+1+1. If I counted all that correctly, there are seven different ways to partition 5. Studying modular forms can be a very efficient way to study certain properties of integer partitions, believe it or not. The connection may not seem obvious at all. On one hand, you have these funny symmetric complex functions, and on the other hand, you’re talking about numbers. How are these related? But that’s the beauty of modular forms.
Q: What classes are you teaching right now?
A: This semester, I am teaching Math 111, the first semester calculus course. And I’m also teaching Math 350, which is called Groups, Rings and Fields — also known as Abstract Algebra. It’s very much an abstract mathematics course that all math majors here must take.
Q: How do you plan to be an active part of the Amherst community?
A: Well, this is just the beginning of my second semester here. One thing that I am planning is to work with some undergraduate students over the upcoming summer. I’m actually seeking applicants to work with me on an original research project over the summer. Any Amherst undergraduate is eligible to apply, although most of them will probably be math majors or thinking about being math majors. I’m absolutely looking forward to working really closely with a group of students on a research problem related to modular forms and partitions.
Q: What hobbies do you pursue in your spare time?
A: I actually play in an adult women’s recreational soccer league. It’s indoor soccer, and we have games every Sunday night, so that is really fun. I do have a very busy schedule here at Amherst, but the soccer league has no practices. I’m actually a bit bruised up right now from my game. It’s not a big time commitment, and it’s recreational, so it’s not as serious as Amherst sports. I’m also big into music, and I like to go see live music. I’m actually into rock and indie rock. I picked up playing the electric guitar in middle school, so that’s another side hobby.
