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A brief review of early and recent advances in Weyl-Dirac Operators

Dirac operators had been at the centre of the attention of Theoretical Physicists for many years, most notably during the years following the publication of Dirac's equation, in 1928. A few decades later, a few mathematicians became particularly interested in this equation and developed related results on first-order elliptic operators on manifolds. In this talk, we'll mostly concentrate on the Weyl - Dirac equation, which is the stationary version of Dirac's equation for massless elementary particles named Weyl - Fermions. This simplification can give interesting insights into the development of electronic devices based on graphene.