Titel: Applications of PDE Compatibility Complexes in Relativity
Startdatum: 16 Mai
Startzeit: 17:15
Stoppzeit: 18:30Uhr
Dr. Igor Khavkine (University of Milan, Milano, Italy) 
Ort: Seminarraum 1403

I will discuss the Killing operator $(K_{ab}[v] = \nabla_a v_b + \nabla_b

v_a)$ on a (pseudo-)Riemannian manifold as an overdetermined PDE and its

(formal) compatibility complex. Such a complex strongly depends on the

geometry of the underlying (pseudo-)Riemannian manifold and is

explicitly known only in very few cases (in particular, in the cases of

maximal symmetry). I will discuss some concrete strategies, based on the

formal theory of PDEs and explicit computer algebra computations, for

the construction of the Killing compatibility complex in some cases of

interest for General Relativity. I will briefly touch on the role of

this complex in the geometry and analysis of tensor wave equations on

curved spacetime in Relativity.