L_infinity algebras, the Batalin-Vilkovisky quantisation, and gauge theory

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The project deals with the underlying mathematical structures of gauge theory. In particular, it has been realised that any Lagrangian field theory has an underlying L_infinity algebra governing its dynamics. L_infinity algebras, also known as strong homotopy Lie algebras, are higher (in the sense of higher category theory) generalisations of Lie algebras. For instance, for L_infinity algebras the Jacobi identity is allowed to hold only up to higher coherent homotopy. The origin of these underlying L_infinity algebras is most easily understood in the Batalin-Vilkovisky quantisation which, in turn, is a generalisation of the Becchi-Rouet-Stora-Tyutin quantisation. Within the context of such algebras it is seen that physically equivalent theories are related by L_infinity quasi-isomorphisms between their underlying L_infinity algebras. The project deals with studies of gauge theory scattering amplitudes, integrability, and renormalisation within this frame work of higher category theory in the context of supersymmetric Yang-Mills theories.