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.
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.