Alex McDonough
About Me:
I am an RTG Postdoctoral Scholar at the University of Oregon working under the supervision of Benjamin Young. Previously, I was a Krener Assistant Professor at University of California, Davis under the supervision of Fu Liu. Before this, I got a PhD in Mathematics at Brown University, advised by Caroline Klivans.
Contact Info:
Email: alexmcd [at] uoregon [dot] edu
Office: MacArthur Court 102
Here's me at the Pontificia Universidad Javeriana in Bogotá, Colombia for the Encuentro Colombiano de Combinatoria (ECCO) in July 2022.
Research Overview:
I study algebraic, geometric, topological, and dynamical combinatorics.
I am especially interested in chip-firing and matroid theory, particularly where the two subjects intersect. More generally, I tend to enjoy any project where I can play around with concrete examples to search for hidden structure. Thankfully, these kinds of projects are plentiful in combinatorics!
One of my favorite aspects of research is figuring out how to get to the heart of a mathematical idea and then present it in an elegant and streamlined way. For particularly intriguing phenomena, I find it helpful to design animations. These are great for presentations, and consistently give me a deeper understanding of the underlying phenomena.
Animation.movHere is my first math animation which I made back in 2020 using Blender. The animation shows a special case of a tiling that I developed in my thesis, which associates elements of the sandpile group of a particular matrix to bases of the associated arithmetic matroid. Thinking about this construction has been incredibly fruitful for my research, since I still haven't found a satisfying answer for why it works that doesn't feel like magic.
You can find my more recent animations in the "presentation materials" tab. While blender is great for 3D animation, my favorite animation tools are SageMath and VSDC.
Personal
Last summer, I got engaged to Julia Schedler, who is currently a statistician at Cal Poly San Luis Obispo! Over the Spring and Summer, I will be working virtually from San Luis Obispo in order to minimize loneliness and rent payments. Here you can find some code that Julia made in order to play around with a tiling construction I have been working on.
One of my favorite hobbies is playing, collecting, and reading about board games. A well written board game instruction manual has many of the same characteristics as a well written research paper (such as clear logic, judicious structure, and plenty of examples). I feel that learning new games has been great practice for learning new mathematics, and teaching rules to others has been great practice for lecturing! If you are curious about my collection, here is my BoardGameGeek Profile.
I also love participating in rec league/ intramural sports whenever I can. I had a great time playing soccer for the math department team in the Fall and am looking forward to a new math department basketball team in the winter!