7 problems

Multifractal-label conjecture. The observed feature reflects the multifractal property of the chaotic system, with each monofractal labelled by $s\in\mathscr{S}$.

Symmetry conjecture for multifractal exponents. The fractal exponents $D_q$ should satisfy a symmetry relation with respect to the critical parameter value $q=\frac{1}{4}$.

Let $\lambda^{\mathrm{GUE}}_n$ be the $n$-th element of the GUE minor process. The peaks and valleys are studied using the gauge functions $(\log n)^{2/3}$ and $(\log n)^{1/3}$, re…

The shell variables are described by a state evolving under the Euler dynamics in the inertial interval. A hidden scaling symmetry is the scaling symmetry represented by equation i…

Multifractality conjecture. The wave functions are multifractal, in deep connection with Anderson localization.

Carpentier–Le Doussal conjecture. The maximum has the asymptotic form

Self-similar time-series conjecture. At least qualitatively, the similarity of observed burst size and duration distributions in solar wind and magnetospheric quantities to those f…