Courant Lecture Series 2011
Courant Lecture Series, April 18-20, 2011
Martin Schlichenmaier (University of Luxembourg) on Berezin-Toeplitz Quantization.
Everybody is invited to attend the fourth Lecture Series of the Courant Research Centre in Göttingen. For any further information about the lecture series please contact Dorothea Bahns.
|April 18, 14:15 - 15:15 Sitzungszimmer||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.
|April 19||More about Berezin- Toeplitz quantization (1)|| The Berezin-Toeplitz quantization (both operator and deformation
quantization) is a quantization scheme addapted 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.
|April 20||More about Berezin- Toeplitz quantization (2)|