Speaker
Semyon Klevtsov, University of Strasbourg
Abstract
In order to model the Quantum Hall effect, the wave functions such as the Laughlin state are often considered on Riemann surfaces. These are N—body holomorphic functions, forming a frame of a vector bundle, which we call Laughlin bundle, over various parameter spaces – jacobian variety, moduli space of complex structures etc. Certain free field path integral helps to produce Laughlin states explicitly. While some of the properties of Laughlin vector bundles (rank, chern character) can be inferred from purely geometric considerations, others, such as existence of projectively flat connection on the Laughlin bundle, require considering Coulomb gas type integrals. I review the subject and report on recent progress. Works in common with I. Burban, P. Wiegmann and D. Zvonkine.