Berezin-Toeplitz Quantization, 19-23 March 2007

Master Class, by Martin Schlichenmaier (Université du Luxembourg)

Overview poster for the Master Classes in 2007

Abstract / "Review":
The Berezin-Toeplitz (BT) quantization scheme supplies simultaneously an operator and a deformation quantization for quantizable Kähler manifolds. Moduli spaces carry often a natural structure of a quantizable Kähler manifold and the BT scheme turns out to be very useful in this context.

The goal of the course is to present the basics of the BT quantization. The geometric set-up will be a Kähler manifold and an associated holomorphic quantum line bundle. The BT operators will be operators on the space of global holomorphic sections of this line bundle and all its tensor powers. It will be shown that in the compact Kähler case the scheme has the correct semi-classical limit (equivalently it is a strict quantization in the sense of Rieffel). Furthermore, a formal deformation quantization adapted to the Kähler structure will be obtained. As intermediate tools (but also of independent interest) Berezin symbols, the Berezin transform and its asymptotic expansion in powers of the quantum line bundle are discussed.

Open problems for further research are presented.

Professor Martin Schlichenmaier will be visiting CTQM from 18 to 31 March 2007.

Review

Link to a review on BT quantization in Advances In Mathematical Physics (open access journal):

Schedule

The schedule for the Master Class is as follows:
Auditorium D3, Bldg. 1531, 2nd floor
Monday 19 March to Friday 23 March:
10:00-10:45 Lecture
10:45-11:15 Coffee break
11:15-12:00 Lecture

On Friday 23 March, there will be a Master Class Dinner.

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List of Participants

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