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Quantum Hall effect is one of the most interesting examples quantum many-particles systems. It occurs in certain two-dimensional electron systems at low temperatures and in high magnetic fields, which exhibit plateaux with the quantized values of the Hall conductance. The Fractional Quantum Hall effect (FQHE), when the Hall conductance takes on fractional values, is an example of the strongly-interacting quantum many-particles. The standard physics approach to the FQHE is to assign a certain many-body wave function to each plateaux. I will talk about a program as to how one can use a combination of probabilistic, asymptotic and geometric methods to learn more about the physics and mathematics of the FQHE wave functions, in particular, describe the electromagnetic and gravitational responses, asymptotics for a large number particles, novel quantized coefficients for the adiabatic transport.

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Semyon Klevtsov, Mathematical Institute, Cologne
TP seminar room 0.03
Contact: Joachim Krug