11 problems

For pseudopotentials corresponding to $1/q$-filling with small $q\in\{2,3,\dots\}$, let $\operatorname{Gap}_{nq}$ denote the excitation gap above the ground-state energy for the sy…

Rational-filling gap conjecture. One may conjecture that

Keski-Vakkuri–Wen conductance conjecture. The conductance of the system is independent of the genus and equal to

Keski-Vakkuri–Wen degeneracy conjecture. For an incompressible multilayer state, the degeneracy of the lowest energy level is

Let the Halperin $\Psi_{331}$ state be a bilayer quantum Hall state, and insert two Laughlin quasiholes into it, one in each layer. Let antisymmetrization be taken with respect to…

Sharp incompressibility conjecture. The same bound should hold under the weaker scale condition

The fractional quantum Hall effect has an area-preserving-diffeomorphism symmetry whose quantum realization involves the Girvin-Macdonald-Platzman algebra. The Magnetoroton is a sp…

Let $N$ particles be described by fully correlated Laughlin-type states, and let $V$ be an external one-body potential. Consider also simpler states obtained from the Laughlin stat…

Let $k$ and $r-1$ be positive integers such that $\gcd(k+1,r-1)=1$, and let $\lambda$ be a $(k,r,N)$-admissible partition, meaning that … Set $\alpha_{k,r}=-\frac{k+1}{r-1}$. The J…

Let $\mathcal{H}=\mathcal{H}_A\otimes\mathcal{H}_B$ be the Hilbert space of a fractional quantum Hall state, with $N_A$ particles in subsystem $A$, $N_B$ particles in subsystem $B$…

Let $p$ be a symmetric polynomial in $n$ variables. Write each symmetrized monomial as a multiset $[l_1,\ldots,l_n]$, and order symmetrized monomials by squeezing: $s>t$ when $t$ c…