EVENT DETAILS AND ABSTRACT


Analysis Seminar

Title: Mathematics of the Quantum Hall Effect
Speaker: Semyon Klevtsov
Speaker Info: Department of Mathematics, Cologne University
Brief Description:
Abstract:

Laughlin states are N-particle wave functions, which successfully describe fractional quantum Hall effect (QHE) for plateaux with simple fractions. It was understood early on, that much can be learned about QHE when Laughlin states are considered on a Riemann surface. I will define the Laughlin states on a compact oriented Riemann surface of arbitrary genus and talk about recent progress in understanding their geometric properties and relation to physics. Mathematically, it is interesting to know how do L.s. depend on an arbitrary Riemannian metric, magnetic potential function, complex structure moduli, singularities -- for a large number of particles N. I will review (both from math and physics perspective) the results, conjectures and further questions in this area, and relation to topics such as Bergman kernels for holomorphic line bundles, Coulomb gases/beta-ensembles, Quillen metric, zeta determinants.

Date: Monday, February 27, 2017
Time: 4:00pm
Where: Lunt 105
Contact Person: Steve Zelditch
Contact email: zelditch@math.northwestern.edu
Contact Phone:
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