Seminario

Strict Deformation Quantization of disk and sphere – a Holomorphic perspective

Seminario del Dipartimento di Matematica
14 dicembre 2023
Orario di inizio 
16:30
Polo Ferrari 1 - Via Sommarive 5, Povo (Trento)
Aula A213 (Povo 1) e via Zoom (contattare dept.math@unitn.it per le credenziali)
Organizzato da: 
Dipartimento di Matematica
Destinatari: 
Comunità universitaria
Comunità studentesca UniTrento
Partecipazione: 
Ingresso libero
Referente: 
Dott. Nicolò Drago
Contatti: 
Staff Dipartimento di Matematica
0461/281508-1625-1701-3898-1980
Speaker: 
Michael Heins (University of Wuerzburg)

Abstract

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.