Pour tout renseignement complémentaire, veuillez contacter les
organisateurs, Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h |
Nicolas Frantz (Angers) |
Scattering theory for some nonselfadjoint operators Abstract: In this talk, we are interested in the scattering theory for an abstract model of nonselfadjoint operators acting on an Hilbert space. The considered operator H is given by a relatively compact perturbation of a selfadjoint operator H0. Under limiting absorption principle assumptions, we explain how the non unitary wave operators associated with H and H0 can be defined and present their properties. Finally, we generalise the notion of asymptotic completeness for these wave operators and relate it to the notion of spectral singularity. These results apply to Schrödinger operators with complex value potentials. |
| 15h15 - 16h15 | Joachim Kerner (Hagen) |
Atypical spectral and transport properties of nonlocally
finite crystals (and maybe more)
Abstract: In the first part of the talk we discuss recent results on Schrödinger operators on periodic graphs which are nonstandard in the sense that we allow vertices to have an infinite number of neighbours. It turns out that such nonlocally finite graphs exhibit various phenomena which are absent in the locally finite setting: and this is true from a spectral as well as transport point of view. Using some explicit examples, we shall illustrate such new effects in more detail. Quite surprisingly, it turns out that one of the examples provides us with a negative answer to a question raised by Damanik et al. in a recent paper on ballistic transport. (this part of talk is based on joint work with O. Post, M. Sabri and M. Täufer. If time allows, we shall also quickly discuss spectral comparison results on discrete graphs. In recent years, various authors have derived such comparison results on Euclidean domains and quantum graphs. Our aim is to present a generalization to the discrete setting. Along the way, we also establish a so-called local Weyl law which is of independent interest. (the second part of the talk is based on joint work with P. Bifulco and C. Rose) |