Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
The Bär-Ballmann framework is a comprehensive framework for considering elliptic boundary value problems for first-order elliptic operators on manifolds with compact and smooth boundary, provided that the induced operator on the boundary is symmetric. There are many operators that satisfy this requirement including the Atiyah-Singer Dirac operator. However, there are interesting operators that do not, with the quintessential example being the Rarita-Schwinger Dirac operator.
In this talk, I'll waggle my chin and rouse up some chalk dust to present recent joint work with Bär, where we drop the symmetry requirement entirely and develop framework to account for general first-order elliptic differential operators.