5 problems

Exceptional-time conjecture. Almost surely, exceptional times at which $\mathcal{C}_t$ contains an unbounded component exist, and the Hausdorff dimension of the random set of such…

Let $\mathfrak{h}_0$ satisfy Assumption, and let $\mathcal{T}_\infty(\mathfrak{h})$ be the set of times at which the KPZ fixed point has non-unique maximizers. Density conjecture.…

Let $F$ be a three-dimensional Bargmann–Fock field on $\mathbb{R}^3$. For each $t\in\mathbb{R}$, let $f^{\mathrm{hor}}(t)$ be the two-dimensional Bargmann–Fock field obtained by re…

Let $\mathsf{\mathscr{E}}$ be the exceptional time set and let $\mathsf{\mu}$ be the associated local-time measure, which is supported inside $\mathsf{\mathscr{E}}$. Full-support c…

Fix $q\in[1,4]$ and let $(\omega_t^{\mathrm{FK}_q})_{t\geq0}$ be the critical infinite-volume heat-bath dynamics on $\mathbb Z^2$. Let $\mathcal E_q$ be the random set of times at…