Presentation

The Center for the Topology and Quantization of Moduli Spaces (CTQM) is situated at the Department of Mathematical Sciences (IMF) at the Faculty of Science, University of Aarhus. The center is directed by Prof. Jørgen Ellegaard Andersen. There are currently 6 permanent members, 8 associated permanent members (attached through the Niels Bohr Visiting Professorship initiative), 5 visiting members, 9 Post Doc's, 19 PhD students, 4 visiting PhD students and 19 associated international collaborators.

The center was created on January 1st 2006, and is 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 with 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.

The center 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.
Chas and Sullivan's discovery of the new structures on the topology of loop spaces of manifolds.
The Andersen-programme which uses the theory of Toeplitz operators on the moduli space of bundles to study topological quantum field theory, and which has resulted in a proof of Turaev's asymptotic faithfulness conjecture.

It is the long-term vision of the researchers in moduli problems to fuse and apply the emerging mathematical frameworks of the above three developments to the mathematical study of quantum field theory and string theory. The center endeavours also to assist in this process, in particular in collaboration and interaction with the Center for Theory in the Natural Sciences at the Faculty of Science, the University of Aarhus.

An active international PhD and postdoc programme is an absolute top priority for the center. The center's activities also include a weekly seminar and an extensive visiting programme for its associated international collaborators and their PhD students and postdocs.

On August 1st 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 has been attached to the center as Visiting Niels Bohr Professor. Besides the permanent researchers at CTQM, the initiative involves a further 4 researchers from IMF and 4 researchers from IFA. These have been attached to the center as associated permanent members.

The Co-ordination Committee for the Niels Bohr Visiting Professorship Initiative consists of

Prof. Jørgen Ellegaard Andersen, Director of CTQM and Researcher in Charge of the Niels Bohr Initiative
Niels Bohr Visiting Professor, Nicolai Reshetikhin
Prof. Henning Haahr Andersen, Director of AALT and Node co-ordinator of LIEGRITS
Prof. Klaus Mølmer, Director of CTN and AU co-ordinator of QUANTOP

The Co-ordination Committee co-ordinates all events under the initiative.

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 description of the planned research co-operation.

Revised 14.06.2007