Hodge Systems with L1 Data and Pauli Hamiltonians

Speaker: Daniel Spector，National Taiwan Normal University   

Inviter: Nguyen Quoc Hung

Title: Hodge Systems with L1 Data and Pauli Hamiltonians

Language: Chinese 

Time & Venue: 2026.05.26  15:00-16:00  Zoom: 373 227 3489 Passcode: AMSS2026 

Abstract: Maxwell's equations model the behavior of the electromagnetic fields which arise from prescribed electric charges and currents.  When one works in the static regime the equations decouple and give separate elliptic systems for the electric and magnetic field.  In three dimensional Euclidean space this system is a div-curl system, while more generally on a manifold it is a Hodge system.  We discuss the equations for the magnetic field, where the natural assumption on the electric current density is that it has finite total mass, as this allows one to model the current carried by a thin wire.  Lebesgue scale estimates for this system (on Euclidean space) were established by Bourgain and Brezis in their foundational CR/JEMS papers in 2004/2007.  In this talk I present some recent work with Felipe Hernandez and Jesse Goodman on sharp Lorentz scale estimates for these equations in both Euclidean space and on a smooth, compact Riemannian manifold.  Aside from being the optimal Lorentz scale inequality, our estimate has an interesting connection with the Pauli Hamiltonian that will also be discussed.