Classification of ground states for critical Dirac equations

In this talk I will present a classification result for critical Dirac equations on the Euclidean space, appearing naturally in conformal spin geometry and in variational problems related to Dirac equations on spin manifolds. Exploiting the conformal invariance, ground state solutions can be classified. This is the spinorial counterpart of the well-known result for the Yamabe equation.

Time permitting, I will also present similar results obtained for conformal Dirac-Einstein equations, consisting of a Dirac equation coupled with a Laplace- type equation.

Joint work with Ali Maalaoui, Andrea Malchiodi and Ruijun Wu.