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05/07/2005, 16:00 — 17:00 — Amphitheatre Pa2, Mathematics Building
, University of Marburg, Germany

Quantization of Complex Domains

In flat Minkowski space, the theory of quantization (coherent states) is fundamental for mathematical physics. In the complex wave representation (Fock space), methods from complex analysis such as Toeplitz operators on Hilbert spaces of holomorphic functions play a basic role. In my talk I will concentrate on two important generalizations: First, the incorporation of curved manifolds, such as symmetric Kaehler manifolds and bounded hermitian symmetric domains, in the theory of quantization, leading to the construction of a unified calculus on Bergman spaces generalizing the Toeplitz-Berezin calculus and the Weyl calculus. Second, the more recent ideas concerning super-symmetry, where one considers super-Hilbert spaces of Grassmann analytic functions and still has a deep theory of quantizations invariant under (super) Lie groups.
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The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.


Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.