Our research group leader, Samantha Fairchild, has been appointed an Assistant Professor at the Technical University of Eindhoven in the Netherlands. We wish her all the best for this significant career step!
Since October 2024, she is a member of the Discrete Algebra and Geometry group. This group plays a leading role in algebraic graph theory, combinatorics, finite and incidence geometry, group theory, discrete Lie theory and applied algebra. Samantha’s research focuses on discrete sets in geometry, often inspired by translation surfaces. She explores using translation surfaces to construct algebraic curves and is also interested in the interplay between dynamics and machine learning.
Samantha earned her PhD in Mathematics from the University of Washington in 2021 before joining our institute as a postdoctoral researcher and W2 Research Group Leader. For her outstanding research, she has been honored with several awards, including the Irene Curie Fellowship from the Technical University of Eindhoven and a Walter Benjamin Fellowship from the German Research Foundation (DFG).
MPI MIS: How did you get into math? What do you find particularly fascinating about this science?
Samantha Fairchild: Though I was good at math in high school, my passion was working with horses. I went to college planning to major in equestrian studies and become a riding instructor, but my mom encouraged me to at least try a better paying and more stable profession, so I signed up to also be a math major since that seemed pretty easy and would allow me to teach math during the school year while having summers free for time with horses. In my second year of bachelor’s studies I took my first proofs based course and that’s when I fell in love with math. In addition to my passion for teaching, I found the art of constructing proofs fascinating, especially when I found unexpected connections.
MPI MIS: Why did you choose this particular field of research?
Samantha Fairchild: I knew I liked Analysis, and really enjoyed my Complex Analysis course during graduate school, so when I asked my professor what options there were he recommended I take a topics course on Translation surfaces. I enjoyed being able to draw pictures to understand what we were working on, and the fact that the field would allow me to use tools from all over mathematics. In addition, I felt that my personality would match well with the instructor, so he became my PhD advisor after that.
MPI MIS: What drives/motivates you in your work?
Samantha Fairchild: Tatiana Toro told me that the best measure of success is learning, and I’ve made that a focus of my work. There is a lot of pressure for results, publications, and getting grants, but the reward and joy I find in learning makes it all worth it.
MPI MIS: Did you ever doubt your abilities as a scientist? Why? How did you handle these situations/feelings?
Samantha Fairchild: In my first year of graduate school I had a panic attack after failing my first midterm. Ever since then waves of feeling inadequate have shown up at every step of my career. I think that imposter syndrome occurs for many people, and it happens because it is so natural for us to compare ourselves to others, but we can only see what they know and not all the things they don’t know, whereas we often focus on what we don’t know. There’s no one way to handle these feelings, but I think the most important thing to do is address them so they don’t negatively affect your life. For me, handling these feelings used a combination of professional counseling, being open with my partner, friends and family, investing in other hobbies, and reminding myself that at the end of the day “mathematician” is just a job, and doesn’t define who I am.
MPI MIS: Did you ever have the impression that it would‘ve been easier/harder if you were male?
Samantha Fairchild: In addition to the inherent advantages to being male in a patriarchal society, there are also people with many other benefits that helped them along the way. My first summer of graduate school was filled with studying for the preliminary exams. I was shocked when some people in the cohort took off the summer from working as a TA in order to study more. For me, I needed money to keep paying off the rent and school loans from my Bachelors so I didn‘t feel I had an option to just miss 3 months of a paycheck to study for exams. There is also an abundance of academics who come from academic families, which gives incredible advantages in terms of the insight into what an academic career looks like. Navigating the persistent question of “but what do you actually do” when describing the life of a mathematics researcher, the isolation from family members who fail to understand the locational mobility required to succeed, all add up to make it harder to stay in the career path. Overall I think it’s important that we each realize that we have advantages and disadvantages, and always be aware of different backgrounds to provide a positive working environment.
MPI MIS: Research usually goes hand-in-hand with teaching, how important is scientific mentorship for you?
Samantha Fairchild: Scientific mentorship is so important, I think as a teacher we send out so much information and ideas into the world, and we just hope something sticks. One of my professors in my Bachelor studies told me that I could do more than just teach math in high school and could get a PhD to teach at the college level. Of all the information she gave me, that is the one piece of advice that got stuck in my mind and changed the trajectory of my mathematics career. Since then each of my collaborators and mentors has given me pieces of advice or comments that stuck with me, helping me to become a better mathematician, a better collaborator, and a better person along the way. I try to share my perspectives and ideas, and make it clear that I’m always around and available for a chat, opening up opportunities for people to use me as one of their mentors as well.
MPI MIS: How does your family/friends regard your career choice?
Samantha Fairchild: They think it’s a bit weird, and don’t really understand what I do. We mainly connect over teaching stories. One of my proudest moments was when my parents were telling their friends that I am actually quite bad at computing tips and taxes since I mainly work with symbols and not with numbers. It was great to realize that the pieces of information I share with them in turn give small changes to other people’s perspective about what a mathematician does.
MPI MIS: Besides mathematics, do you have any other passion that makes you happy?
Samantha Fairchild: I love riding horses, and have found a place to ride a horse at least once per week in every single place I’ve lived. I also have two lovely cats for which I am passionate about being the best cat parent ever.
A central theme of my research is the analysis of discrete sets associated with geometric objects, such as translation surfaces. The first example of a translation surface is a torus, which is like the surface of a donut. Suppose I want to decorate my donut with a geodesic line of icing which makes a closed loop. In this case, each of my possible decorative lines can be measured in terms of the displacement, that is how many times the icing went around the hole, and how many times it went around the cake. So for each line I’ll get two integers, and I can represent all possible configurations by a pair of integers, which is a discrete subset of the plane. In the case of the torus we can use number theory to study the possible icing loops. However once we start working with donuts that have multiple holes, we have more interesting results, so studying our icing loops uses techniques coming from dynamics, number theory, and geometry as well.