Interactive Tools for Integrable Dynamical Systems

Faculty Member

Thomas Nevins

While the dynamics of particles moving in space have been studied for a long time, the second half of the 20th century saw the discovery of new particle systems that have many conserved quantities: they are "integrable systems." It was later discovered that there is a beautiful interplay between the dynamics of particle collisions and subtle geometric features of the phase space of a system. In this project, students will master some basics of some important particle systems, starting from the Calogero-Moser system and proceeding, as time permits, to its relativistic analogue (the Ruijsenaars-Schneider system) and perhaps further; and will build interactive computer simulations of these systems to help students and researchers visualize and investigate the properties of these systems.

Team Meetings

Weekly

Project Difficulty

Intermediate

Undergrad Prerequisites

Some knowledge of matrix algebra/linear algebra at the level of Math 225 or the first half of Math 415/416 is expected. Experience writing code in some language is expected.