Probing and Exploring Higher-Form Topology in Three Dimensions: From Light to Quantum Geometry and GMP Algebra

University of Coimbra

I will discuss some recent works of mine on higher-form topology in three-dimensional quantum matter, moving from optical probes to quantum geometry and, finally, to a generalized GMP-algebra framework. I will begin with topological optical chirality dichroism, where chiral light directly probes topological structure through a distinctive optical response. I will then turn to the experimental realization of tensor singularities and their Euler-class descendants in superconducting circuits, revealed through measurements of non-Abelian quantum geometry. Finally, I will present a formal perspective based on three-dimensional quantum Hall fluids of extended objects, in which a generalized GMP algebra is related to the underlying higher-form topology.