Strict Deformation Quantization of disk and sphere – a Holomorphic perspective

Seminario del Dipartimento di Matematica
14 dicembre 2023
Orario di inizio 
Polo Ferrari 1 - Via Sommarive 5, Povo (Trento)
Aula A213 (Povo 1) e via Zoom (contattare per le credenziali)
Organizzato da: 
Dipartimento di Matematica
Comunità universitaria
Comunità studentesca UniTrento
Ingresso libero
Dott. Nicolò Drago
Staff Dipartimento di Matematica
Michael Heins (University of Wuerzburg)


We discuss recent joint work with Annika Moucha and Oliver Roth on strict deformation quantization of the Poincaré disk D and the Riemann sphere Ĉ. It turns out that both geometries and their strict deformation quantizations may be naturally understood as embedded in the second configuration space of the sphere {(z,w) {(z, w) ∈ Ĉ2: z ≠ w}. It carries the structure of a complex Riemannian manifold and allows to unify both theories in many regards. This shift of perspective moreover allows to work with holomorphic objects instead of merely real--analytic ones and admissibility of observables directly corresponds to their domains of definition. We provide explicit formulas for the convergent star product, discuss its asymptotic expansion for h → 0 within a sector and analyze its symmetries. Finally, we give an outlook on how the spectral theory of the Laplace-Beltrami operator fits into the emerging framework.