# Analysis Seminar

#### Geometry and Large N Asymptotics in Laughlin States.

**Speaker:**
Semyon Klevtsov, University of Cologne

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, March 9, 2017, 11 a.m.

**Synopsis:**

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 Coulomb gases/beta-ensembles, Bergman kernels for holomorphic line bundles, Quillen metric, zeta determinants. The talk will be friendly to nonspecialists.