Organizers: Jean Bellissard and Peter Hislop

17-19 March 2006, University of Kentucky, Lexington, Kentucky

This is an intensive, three-day workshop on transport properties of Schrödinger operators with random potentials and related problems of transport theory. The focus will be on topics of recent research including linear response theory and kinetic equations, noncommutative geometry and the quantum Hall effect, edge and bulk conductivities, the Kubo formula for conductivity, classical and quantum diffusion, and other transport phenomena in random media. The workshop consists of hour-long expository talks by leading researchers in random Schrödinger operators and transport theory, short talks by new researchers in the field, a poster session, and round table discussions on open problems and new directions.

The last decade has seen major advances in the analysis of the operators that describe the propagation of quantum particles, like electrons, and of acoustic and electromagnetic waves, in random media. There have been advances in the understanding of Anderson localization, propagation properties of random Schrödinger operators, and the development of quantum diffusion in the long-time behavior of quantum dynamics. Deeper properties, such as conductivity and linear response theory are now being actively investigated. The goal of this workshop is to bring together a group of experts in all aspects of these problems in order to exploit these recent advances. The major emphasis of the discussions of this workshop will revolve around the following issues and open problems: Noncommutative Geometry and the Quantum Hall Effect; The Kubo Formula: Relaxation Time Approximation and Linear Response Theory ; Mott Conductivity for Random Systems; Quantum Diffusion and kinetic equations; The relaxation time approximation. Transport near the Anderson Metal-Insulator Transition; Transport for Random Landau Hamiltonians.

The following mathematicians have accepted our invitation to speak at the conference:

• David Damanik (Caltech)
• Gian Michele Graf (ETH Zurich, Switzerland)
• Francois Germinet (Université de Cergy-Pontoise, France)
• Yulia Karpeshina (University of Alabama, Birmingham)
• Abel Klein (University of California, Irvine)
• Frederic Klopp (Universite Paris 13, France)
• Michael Loss (Georgia Institute of Technology, Atlanta)
• Olaf Post (University of Kentucky)
• Jeff Schenker (IAS, Princeton)
• Hermann Schulz-Baldes (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany)
• Gunter Stolz (University of Alabama, Birmingham)
• Dominique Spehner (Université Joseph Fourier, Grenoble, France)
• Simone Warzel (Princeton University)

Funding

This workshop is supported by the Institute for Mathematics and its Applications as an IMA Participating Institution conference, the Department of Mathematics of the University of Kentucky, the Department of Mathematics of the Georgia Institute of Technology, the Office of the Executive Vice-President for Research at the University of Kentucky, and the National Science Foundation, Division of Mathematical Sciences.

Funds are available to support participants. Priority will be given to students and recent Ph.Ds as well as researchers from underrepresented groups. Participants from participating institutions of the IMA may obtain financial support from their PI funds.

For further information, please contact either Jean Bellissard or Peter Hislop.

Registration form

Please take a moment to fill in the registration form. A block of nonsmoking rooms have been reserved at the University Inn (1229 South Limestone Street, Lexington, KY (859)-278-6625) for workshop participants until 15 February 2006. If you tell us your arrival and departure dates, we will be happy to make a room reservation for you.

Invited Participant Registration