April 16, 2021.
Classification of Ground States for Critical Dirac Equations.
In this talk I will present a classification result for nonlinear Dirac equations with critical nonlinearities on the Euclidean space. They appear naturally in conformal spin geometry and in variational problems related to critical Dirac equations on spin manifolds. Moreover, two-dimensional critical Dirac equations recently attracted a considerable attention as effective equations for wave propagation in honeycomb structures. Exploiting the conformal invariance of the problem ground state solutions can be classified, in analogy with the well-known result for the Yamabe equation. This is a joint work with Andrea Malchiodi (SNS, Pisa) and Ruijun Wu (SISSA, Trieste).