120 credits in mathematics and/or physics. Participation in Mathematical Methods of Physics II or Differential topology. Symmetry and Group theory in Physics or Algebraic Structures. Analytical mechanics. Complex analysis.
In this course you will explore the interplay between representation theory and integrable systems, and through this gain a deeper understanding of their mathematical structures and applications in physics. Topics include Schur-Weyl duality, representations and characters of classical Lie algebras, affine Kac-Moody algebras, Hopf algebras, and symplectic geometry as a framework for Hamiltonian mechanics. You will study integrable systems, including classical and quantum examples, and techniques such as the Yang-Baxter equation, S-matrices, and spin chain Hamiltonians. Emphasis is placed on using representation theory for spectral calculations and applying integrability methods to physical models.
