Hi! My name is Jonathan and I am a postdoc at the Centre de Recherches Mathématiques in Montreal. I am based at McGill and at Laboratoire de combinatoire et d’informatique mathématique (LACIM) at UQAM. Previously, I held a postdoc at the Max Planck Institute for Mathematics in the Sciences. I was part of both the Nonlinear Algebra Group and the Geometry, Groups and Dynamics Group. I did my PhD at Harvard, where I was advised by Lauren Williams. During my undergrad, I studied math and physics at McGill. 

My research focuses on relating combinatorics and algebraic geometry, especially with an eye towards positivity phenomena. A few key areas of interest are: Flag varieties, positroids, tropical geometry, cluster algebras, positive geometries and the amplituhedron. 

The Grassmannian is a manifold that occurs in many areas of mathematics. There is a natural combinatorial way to break it into pieces. However, we know that the way these pieces interact with each other can be arbitrarily complicated. Fortunately, there is a special subset of the Grassmannian, the positive part, which behaves much better. It turns out that the positive part of the Grassmannian, and in fact, the positive parts of many other spaces, lead to interesting insights into matroid theory, cluster algebras and tropical geometry. Moreover, the positive Grassmannian is of great interest to physicists working on N=4 super symmetric Yang-Mills theory and is a key motivation in the growing study of positive geometries.