Title: The Boson Fermion Correspondence Description: Fundamental particles in quantum physics are partitioned into two types, called bosons and fermions, depending on how they behave under being permuted. The wave function of a collection of identical bosonic particles is invariant under any permutation of these particles, while the wave function of a collection of identical fermionic particles is multiplied by the sign of the permutation. Despite the seemingly physics focused introduction to this project, no prior knowledge of quantum physics is required. However, it can help provide background motivation and context. The goal of this project is to explore and understand surprising combinatorial identities between the quantum field theories of free bosons and free fermions. This will be done by first learning about the symmetry structures, called vertex operator algebras (essentially a generalisation of a ring), underlying these two field theories, studying their modules and constructing suitable isomorphisms, which imply interesting combinatorial identities.

Code: SW2122B

Type: Double

Supervisor: Dr S. Wood

Prerequisite modules: MA2013 Groups, MA3014 Algebra II: Rings

Maximum number of students: 1