Abstract In this series of lectures, we will introduce a fundamental correspondence at the intersection of representation theory, geometry, PDEs, and physics called the boson-fermion correspondence. However, rather than the classical case, we will describe a deformed version, and while this is seemingly (significantly) more difficult, the deformation essentially only appears in one computation early on, and otherwise the proofs and formulas remain unchanged. After going through this construction in general, we will proceed to discuss special cases in the final lecture, with an emphasis on the combinatorial connections.
arXiv References: 1212.6049, 2410.06582, 2502.02841.