Séminaire: Problèmes Spectraux en Physique Mathématique

Année 2025-2026

Pour tout renseignement complémentaire, veuillez contacter les organisateurs, Hakim Boumaza, Mathieu Lewin ou Stéphane Nonnenmacher.

14h - 15h	Constanza Rojas-Molina (Cergy)	Eigenvalue statistics and (de)localization for randomly perturbed long-range hopping operators Abstract: We report on recent work on the spectral and dynamical properties of operators with (weakly) decaying long-range hopping terms with diagonal disorder of Anderson type. We show that under certain conditions on the parameters of the model, the operator exhibits a form of dynamical delocalization in a region of the spectrum where pure point spectrum and Poisson eigenvalue statistics hold. These results apply in particular to the discrete fractional Anderson model, under certain conditions on the fractional exponent and the strength of disorder. This is joint work with P. Hislop (Kentucky) and R. Matos (PUC Rio).
15h15 - 16h15	Clément Tauber (Paris-Dauphine)	Index of a pair of pure states and interacting integer quantum Hall effect Abstract: We introduce the index of a pair of pure states on a C*-algebra, which generalizes the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall conductance associated with an invertible state of a two-dimensional interacting electronic system may be written as the index of a pair of pure states by inserting a unit of magnetic flux. This exhibits the integrality and continuity properties of the Hall conductance in the context of general topological features of the index. Based on joint work with J. Shapiro (Princeton) and S. Bachmann (UBC Vancouver).

Octobre 2026