Third year undergraduate James Goodwin has been selected to be one of the speakers in the Tomorrow’s Mathematician Today 2013 Conference.  The conference will be held on Saturday 16 February at the University of Greenwich, and is sponsored by IMA and GCHQ.  James’ talk will be based on his summer 2012 project on “Lie Algebras and Quantum Mechanics” sponsored by the Nuffield Foundation and supervised by Allessandro Torrielli.  The accepted abstract of the talk follows: the talk will look at the connection between areas of Lie theory and quantum mechanics.  Assuming only a familiarity with matrix manipulation, the concept of a “Lie Algebra” will be introduced and used to compare classical simple harmonic with the quantum harmonic oscillator.  The talk will then explore the canonical form of Pauli matrices and how they are applied to the quantum-mechanical concept of spin.  The talk will finish with a brief non-technical description of how Lie algebras occur in a problem at the frontier of theoretical physics – the Yangian algebra associated with the anti-de-Sitter/conformal field theory correspondence.