I’m in my sixth year as an Assistant Professor of Mathematics at Williams College.  I received a BA in Mathematics and Statistics from Williams College in 2010, and received my PhD in Mathematics in 2015 from UC Berkeley, where my advisor was Bernd Sturmfels.  I also spent a year in Stockholm, Sweden as a postdoc at KTH.

Ralph Morrison standing next to a statue of the number zero.

Me and my favorite multiplicative identity (or additive, if you want to be non-tropical about it)

My research lies mainly in the world of algebraic geometry, which studies sets of points that solve polynomial equations. Such a solution set is called a variety.

In particular, I work on tropical geometry, which is a “skeletonized” version of algebraic geometry. We can take a classical variety and “tropicalize” it, giving us a tropical variety.  This turns out to be a piecewise-linear subset of Euclidean space, with lots of cool geometric properties. Tropical geometry combines combinatorics and discrete geometry with classical algebraic geometry, and allows for developing theory and computations that tell us about the classical varieties.

I also study computational algebraic geometry, which uses various algorithmic tools to better study the geometry of varieties. I’m especially interested in this area when working over non-Archimedean fields, like the p-adics.

When I’m not teaching or working on mathematics, I like running,playing board games (I’m good at Dominion, not so good at Settlers of Catan), hosting or participating in trivia, and coming up with alternate mascots for various institutions.