Bridging Representation Theory and Matroid Theory Through Infinite-Dimensional Grassmannians

This project focuses on the connection between matriod theory and representation theory via their shared connection to Grassmannians. Much of the information we know has been derived using combinatorial models, including matroids and triangulations of surfaces. In particular, combinatorics have been invaluable in the study of cluster algebras and cluster categories. This PhD project will extend the existing relationship between matriods and finite-type cluster algebras to similar types of infinite-dimensional structures. Any progress in this project will be a fundamentally new connection for the infinite-dimensional Grassmannian. Among the challenges to overcome is viewing these structures in new ways that doesn’t rely on a finite/discrete perspective. Applications include studying the recently-proposed infinite-dimensional amplituhedron in high energy physics.

Keywords:Matroid Theory, Grassmanians, Cluster Categories

Disciplines:Algebraic geometry, Commutative rings and algebras, Convex and discrete geometry

Project type:PhD project