Geometry of Quantum Hall States
Organized by Sasha Abanov, Tankut Can, Anton Kapustin, and Paul Wiegmann
April 18, 2016 – June 17, 2016
The quantum Hall effect (QHE) is a fascinating and important phenomenon. Since its experimental discovery in the early 80’s the QHE continues to fuel work in experimental physics, metrology, fundamental theoretical physics and mathematics.
At very low temperatures and strong magnetic fields, highly entangled collective electronic quantum states are formed on surfaces of ultra clean doped semiconductors. Despite varying microscopic details and imperfections of materials, these states possess universal properties demonstrating very precise (up to 9 significant digits) quantization of the Hall conductivity in units of fundamental constants. Other observable features are: an excitation gap determined by electron interactions, fractional charge and statistics of elementary excitations, and chiral massless boundary modes with universal dynamics.
Many universal features of the QHE are also captured at the microscopic scale by model electron wave functions. An outstanding theoretical task is to connect this microscopic description with the macroscopic picture discussed above.
Recently, the physics of low energy transport phenomena has been connected to the response of the ground state to variations of the spatial geometry. This observation has led to a geometric description of QHE states, which links the physics of QH states to problems of modern geometry (Kahler geometry). Another rapidly developing link is a relation between the FQHE and the theory of random geometry and quantum gravity. The synthesis of subjects and intriguing links to modern mathematics give the QHE a very special status.
The goal of the program is to bring together physicists and mathematicians working on topics related to the geometry of QH states, in order to develop a geometric approach to quantum Hall states. The program will also encourage a broader discussion of the role of geometry in quantum states of condensed matter systems. Some of the key topics of the program are:

QH wave functions in geometric backgrounds

Effective field theory and geometric responses of QH states

Transport properties in inhomogeneous backgrounds

Bulkboundary correspondence of QH states

Entanglement and topological order in QH states

Hydrodynamics of fractional QH electronic fluid

Methods of Conformal Field Theory and QH states

Other topics and connections to other systems (anomalous hydrodynamics, quantum gravity, random matrices, Kahler geometry)
Speaker and Seminar Schedule:
The weekly talks take place on Mondays, Wednesday and Fridays at 10:30am in room 313.
Date and Time  Title  Presenters 
4/25 at 10:30am – Room 313  Galilean invariance at quantum Hall edge  Sergej Moroz 
4/27 at 10:30am – Room 313  Towards the classification of gapped phases of matter  Ryan Thorngren 
4/29 at 10:30am – Room 313  Noncommutative geometry techniques for aperiodic condensed matter systems  Emil Prodan 
5/2 at 10:30am – Room 313  Geometric deformation and Berry curvature in quantum Hall states  Barry Bradlyn 
5/4 at 10:30am – Room 313  The holographic Weyl semimetal  Karl Landsteiner 
5/4 at 1:00pm – Room 313  Mathematical physics of map enumeration  Peter Zograf 
5/6 at 10:30am – Room 313  Electromagnetic response of semimetals from wavefunction geometry and topology  Joel Moore 
5/9 at 10:30am – Room 313  CANCELLED  
5/10 at 10:30am – Room 313  Hall viscosity from Hall conductivity in Dirac crystals  Maria A. H. Vozmediano 
5/11 at 10:30am – Room 313  Anyons from braiding fluxes in the Pauli Hamiltonian  Yosi Avron 
5/13 at 10:30am – Room 313  CANCELLED  
5/16 at 10:30am – Room 313  The Nematic Fractional Quantum Hall State and the interplay of Geometry and Topology  Eduardo H Fradkin 
5/18 at 10:30am – Room 313  Geometric Defects in FQH states  Andrey Gromov 
5/20 at 10:30am – Room 313  CANCELLED  
5/23 at 10:30am – Room 313  Fractional Quantum Hall Effect on Singular Surfaces  Misha Laskin 
5/25 at 10:30am – Room 313  Hydrodynamics with nonAbelian currents: from spin Hall effect to quarkgluon plasma  Piotr Surowka 
5/26 at 2:00pm – Room 313  Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics  Alexei Tsvelik 
5/27 at 10:30am – Room 313  Absolute Stability without Topological Order  Shivaji Sondhi 
6/1 at 10:30am – Room 313  Jack Polynomials as Quantum Hall States  Boris Hanin 
6/3 at 10:30am – Room 313  Questions around Laughlin states on Riemann surfaces  Semyon Klevtsov 
6/6 at 10:30am – Room 313  CANCELLED  
6/8 at 10:30am – Room 313  Questions around Laughlin states on Riemann surfaces, part 2  Semyon Klevtsov 
6/10 at 10:30am – Room 313  Hydrodynamics with Hall viscosity: variational approach  Alexander Abanov 
6/13 at 10:30am – Room 313  CANCELLED  
6/15 at 10:30am – Room 313  NewtonCartan geometry and hydrodynamics with Hall viscosity  Gustavo Monteiro 
6/16 at 1:30pm – Room 313  Formalism for the solution of quadratic Hamiltonians with large cosine terms  Sriram Ganeshan 
6/17 at 10:30am – Room 313  Quasielectrons on the sphere and jack polynomials  Boris Hanin 