John McAlister

About me

I am John McAlister, a PhD candidate studying applied math at the university of Tennessee - Knoxville. I am a member of the Fefferman lab under the direction of my co-advisor Dr. Nina H. Fefferman. I am also co-advised by Dr. Tadele Mengesha. Before I came to the University of Tennessee, I did my undergraduate work at The Ohio State University (go Bucks) where I earned a B.S. in mathematics and a B.S. in zoology.

When I started my academic journey, I thought that I wanted to be an ecologist or a zoologist because I loved learning about the ways animal assemblages interacted. As I learned more, I realized the animal systems themselves were not the interesting part to me, rather the mathematical descriptions of the interactions. Naturally, this led to me studying Mathematical biology and, in particular, game theoretic modeling.

My research

Currently, I study game theoretic modeling with explicit spatial or relational structure. I like thinking about these kinds of questions in all sorts of application areas, from ecology to economics. The use of dynamic game theory has been hugely important to modelers in behavioral ecology and economics for many years. The part that I am interested in is the way that explicit relational structure impacts the dynamics of dynamic games.

This can mean several different things but in the case of games with a discrete player space, it looks like determining which networks of interaction can promote different equilibria. In this work I use graph theory and elementary game theory to work out analytical solutions to problems involving relational structure and equilibria.

In continuous domains, this looks rather different. Instead of thinking about players as individuals who are connected in a particular network, we can also think of them as elements of a continuous domain where interactions between players are determined by some integrable kernel. In this case, the shape of the kernel and the shape of the domain can have real impacts on the kinds of equilibria that may result from dynamic games. I find this setting so exciting because it can turn complicated, spatially explicit, dynamic games into PDEs and non-local equations. This is where my current interests are focused. The use of non-local equations in dynamic game theory is rather new and not often used to describe continuous sets of players. However, the theory of non-local equations offers a wonderful tool set for the analysis and visualization of dynamic game processes in continuous settings.

Throughout all of this, I try to include numerical methods, to make sure that the analytical results can be observed and understood in application areas and in systems where analytical solutions are impossible. To that end, I often use python and MATLAB to write simulations and code numerical methods to analyze the models I work on.

In addition to my work on dynamic games, I have also been a part of research in pandemic ecology, graph theory, behavioral ecology, and more. You can find a full list of these projects linked here.

My teaching and mentorship

I have had the opportunity to teach both during my time as an undergraduate and as a graduate student. At the University of Tennessee, I have had the privilege of teaching Math 119, Math 125, and Math 113.

Outside of those courses, I have also had the opportunity to mentor undergraduate research and am currently leading an undergraduate research project with a very talented student studying hybrid modeling and the theory of planned behavior.

My life outside of academia

Beyond academia, I make it my goal to take up at least one new hobby every year. (You think that I’m joking but my New Years Eve parties often involve a hobby brainstorming session). This means that I go through hobbies quickly but there are a few that have stuck around.

Since my time in undergrad, I have enjoyed powerlifting on and off. I really enjoy the routine of going to the gym and lifting in the mornings. During my first years in graduate school, I also took up running. I love to run when the weather is nice, and I am proud to say I have run a marathon and several halves during my time in graduate school.

Those two hobbies have stuck around longer than the rest, by I also go through rock climbing phases, cycling phases, and quilting phases. Additionally, I love to follow college football (again go Bucks) and college basketball.