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Welcome to CTQM

CTQM

The center for the topology and quantization of moduli spaces (CTQM) is based at the Department of Mathematical Sciences at the Faculty of Science at University of Aarhus. It was created on January 1st 2006 based on a grant from the Danish Natural Science Research Council.

The center focuses on the investigation of the topology and quantization of moduli spaces associated to two-dimensional surfaces and their mapping class groups.

It is a collaborative project involving algebraic topology, algebraic geometry, Riemann surface theory, gauge theory and Berezin-Toeplitz quantization.

We will pursue the significant new research opportunities arising from three recent important developments:

  • The Madsen-Weiss proof of the famous conjecture of Mumford on the stable cohomology of the moduli space of curves.
  • The discovery by Chas and Sullivan of the new structures on the topology of loop spaces of manifolds.
  • The Andersen-programme of using the theory of Toeplitz operators on the moduli space of bundles to study topological quantum field theory, which has resulted in a proof of Turaev's asymptotic faithfulness conjecture.

August 1 2006 the center considerably extended its activities through the Niels Bohr Visiting Professorship initiative of the Danish National Research Foundation. Professor Nicolai Reshetikhin from University of California, Berkeley, has been attached to the center as Visiting Niels Bohr Professor.

The scientific co-operation behind the Niels Bohr initiative is within the fields of Mathematics and Theoretical Physics. It involves quantum topology and quantization of moduli spaces, quantum algebras and their representations, statistical mechanics related to quantum gauge theory and string theory, cosmological aspects of string theory together with the relation between quantum information theory, quantum optics and topological quantum field theory.

For more information see the Center Presentation.

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Revised 06.05.2016

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