Courant Lecture Series 2011

Courant Research Centre Higher Order Structures in Mathematics


Martin Schlichenmaier (Luxembourg):

Berezin-Toeplitz Quantization of Moduli Spaces

April 18 - 20, 2011


Programme: Monday April 18, 14:15 - 15:45:
Berezin-Toeplitz Quantization of Moduli Spaces
As was shown by Bordemann, Meinrenken, and Schlichenmaier the Berezin-Toeplitz (BT) operator quantization and its associated star product give a unique natural quantization for a quantizable compact Kaehler manifold. In the talk an overview over BT quantization is given. The procedure is applied for the moduli space of gauge equivalence classes of SU(N) connections on a fixed Riemann surface. In the language of algebraic geometry this moduli space is the moduli space of semi-stable vector bundles over a smooth projective curve. In this context the Verlinde spaces and the Verlinde bundle over Teichmueller space show up. Recent results of J. Andersen on the asymptotic faithfulness of the representation of the mapping class group on the space of covariantly constant sections of the Verlinde bundle are presented.
Tuesday April 19, 10:15 - 11:45:
More about Berezin- Toeplitz Quantization I
Wednesday April 20, 12:30 - 14:00:
More about Berezin- Toeplitz Quantization II
The Berezin-Toeplitz quantization (both operator and deformation quantization) is a quantization scheme adapted to Kaehler manifolds. In these two lectures I will define the basics of the scheme in detail and indicate some points of the proof that it is indeed a quantization for the compact Kaehler manifold case. If time permits I will cover also coherent states, symbols and the Berezin transform.


The first lecture takes place within the Born-Hilbert-Seminar and can be attended independently of the following two.

All lectures will be given in the Sitzungszimmer in the main building of the Mathematical Institute, Göttingen University, Bunsenstr. 3-5, Göttingen. Travel info.


Dinner: You are welcome to join us for dinner on Monday night. It is not necessary to sign up beforehand, but it would be nice if you could let us know if you plan to attend (mail to ).


Poster


Back to:   [D. Bahns]   [Mathematical Institute]   [Courant Research Centre Mathematics]