16 problems

Let $\gamma\in(1/\sqrt{2},\sqrt{2})$, let $\mu_\gamma$ be the Gaussian multiplicative chaos measure on $[0,1]$ with parameter $\gamma$, and let $c_n$ be its $n$-th Fourier coeffici…

Let $D\subset\mathbb{R}^d$ and let a log-correlated Gaussian field on $D$ admit a smooth white noise decomposition. Denote its derivative Gaussian multiplicative chaos by…

Beltrami-welding conjecture. The above Beltrami welding yields an SLE loop measure and thus an independent second construction of the SLE loop in Theorem 1.3 of Ang (2021).

Dual degenerate insertion conjecture. For every real $p<\frac{4}{\gamma^2}$,

Let $\omega_{\mu,\varepsilon}(u)$ be the regularized Gaussian field and define its centered version by … For $-1/\mu-1/2<\operatorname{Re}(q)<2/\mu$, and for a test function…

Let $\widetilde{\omega}_{\mu,\varepsilon}(s)$ be a Gaussian process whose covariance agrees with the covariance in Eq. up to $O(\varepsilon)$ as $\varepsilon\to0$, and whose mean a…

Self-duality conjecture. Under $\tau\mapsto1/\tau$ and $q\mapsto q/\tau$, it satisfies

Infinite divisibility conjecture. The distribution of

Morris distribution conjecture.

Selberg distribution conjecture. Its distribution has Mellin transform

Let $\mathcal{T}_{N}$ be the set of triangulations of the sphere with $N$ faces, and let $\mathcal{T}_{N,3}$ be the set of triangulations with $N$ faces and three marked faces. Equ…

Triple-point conjecture. As $\varepsilon\to0$,

Inner phase II conjecture. The following convergence in law holds:

Supercritical renormalization conjecture. As $\varepsilon\to0$,

Let $\alpha e0$ and let $\gamma^2trianglelefteq2d$ describe the parameters in the lognormal star-scale invariant setting; $M$ denotes a solution random measure. **Solutions conjectur…

Power-law spectrum conjecture. The moments of $M$ satisfy