Title: Quantum Hall effect and Kähler metrics
Speaker: Semyon Klevtsov, University of Cologne
Date: Monday, April 21, 2014
Time: 4:00pm-5:30pm
Place: Seminar Room 313, Simons Center
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Abstract: In physics, important information about a system sometimes can be obtained by studying its response to geometry. Recently, the gravitational response of the Quantum Hall effect on Riemann surfaces attracted considerable attention. I will begin by explaining that the problem can be formulated naturally using Kähler metrics, line bundles and projective embeddings. Then I will explain how to fully constrain the large N expansion of the QHE partition function on Riemann surfaces (and on Kähler manifolds) by relating it to the Bergman kernel, extending previous math (S. Donaldson, R. Berman) and physics (P. Wiegmann – A. Zabrodin) results. Then I will discuss the meaning of Liouville and Mabuchi functionals, appearing in the large N expansion. I will also discuss possible extension of these results to the case of fractional QHE. (Based on arXiv:1309.7333)