## Analysis/PDE Reading Seminar

**Date:** November 7, 2017

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 624

**Speaker:** Boris Hanin, TAMU

**Title:** *Introduction to the Quantum Hall Effect*

**Abstract:** The Quantum Hall effect concerns the low temperature behavior of many electrons confined to a two dimensional sample, such as the surface of a semi-conductor, and subjected to a strong perpendicular magnetic field. In their seminal experiments in the early 1980’s, Von Klitzing-Dorda-Pepper and Tsui-Stormer-Gossard discovered that the so-called Hall conductance is robustly and precisely quantized. This lead to much to much work so-called topological phases of matter and topological insulators. In this talk, I will give a gentle introduction to the QHE, with a focus on the basic examples. I will then briefly describe what is known about the partition function for the simplest and most important QHE wavefunction introduced by Laughlin. I will end with an open question about partition functions for important generalizations of the Laughlin wavefunctions, called incompressible states boundaryless states. The analysis of these wavefunctions is thought to involve conformal field theory and topological recursion in more than one dimension.