Aktualności — Wydarzenia
North Atlantic Noncommutative Geometry Seminar
SPECTRAL METRIC AND EINSTEIN FUNCTIONALS
Prelegent: LUDWIK DĄBROWSKI
2022-11-16 17:15
Using the Wodzicki residue, in terms of the Laplace operator, we define two bilinear functionals on vector fields. Their densities yield, respectively, the metric tensor and the Einstein tensor on an even-dimensional Riemannian manifold. Then, in terms of the Dirac operator, we define two bilinear functionals on differential forms. Their densities, in turn, yield the contravariant metric tensor and the Einstein tensor on an even-dimensional spin manifold, respectively. We generalise these concepts to non-commutative geometry. In particular, we prove that the Einstein functional vanishes for the conformally rescaled geometry of the noncommutative two-torus.
2022-10-05
Tomasz Maszczyk
Nie jesteś zalogowany | zaloguj się
