Research summary
The scattering amplitudes problem in physics involves describing what happens when elementary particles scatter off of each other. A clear understanding of these amplitudes is needed to analyze data from particle accelerators, such as the Large Hadron Collider. The current approach to the problem involves constructing a geometrical object that contains the essential elements of the answer encoded within it.
As Canada Research Chair in Algebra, Combinatorics and Mathematical Computer Science, Dr. Hugh Thomas is constructing and studying two geometries that encode the structure of a cluster algebra. For the first geometry, he and his research team will construct a polytope that generalizes the associahedra of finite-type cluster algebras to other cluster algebras. The second geometry is a variety that similarly generalizes the cluster configuration spaces of finite-type cluster algebras. Understanding these geometries will not only shed light on the scattering amplitudes problem, but will also increase our understanding of the quantum field theory in theoretical physics.