Speaker: Ali Maalaoui (MIT)

Title: The Conformal Fractional Dirac Operator and the Fractional Spinorial Yamabe problem.

Abstract:

I will first discuss the classical Spinorial Yamabe problem and its geometric relevance. Then I will review the construction of conformally invariant powers of the Dirac operator. I will focus in particular on the Caffarelli and Silvestre type extension and the renormalized energy expansion in the fractional setting. I will also address the construction of a Q-curvature operator in the critical case emphasizing the similarities with the case of differential forms.