Quantised Higher Gauge Theory

Lorenzo will investigate the quantisation of higher gauge theory. In particular, he will study the underlying mathematical structures such as higher category theory, L infinity algebras and quasi-isomorphims, Q-manifolds, quasi-groupoids, higher principal bundles and connections, and twistor geometry. He will then analyse the full BV quantisation procedure of higher gauge theory. He will further supersymmetrise the setting and study the localisation of higher Chern-Simons theory. He will also compute partition functions and other relevant objects and discuss applications in mathematics and physics.